sklearn-classifiers-tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scikit-learn Classification Algorithms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "According to [Mitchell](http://www.cs.cmu.edu/~tom/mlbook.html), machine learning is ”concerned with the question of how to construct computer programs that automatically improve with experience.” [Machine learning](https://en.wikipedia.org/wiki/Machine_learning) is interdisciplinary in nature, and employs techniques from the fields of computer science, statistics, and artificial intelligence, among others. The main artifacts of machine learning research are algorithms which facilitate this automatic improvement from experience, algorithms which can be applied in such diverse fields as computer vision, artificial intelligence, and data mining.\n",
    "\n",
    "[Classification](https://en.wikipedia.org/wiki/Statistical_classification) is concerned with building a model that separates data into distinct classes. This model is built by inputting a set of training data for which the classes are prelabeled in order for the algorithm to learn from. The model is then used by inputting a different dataset for which the classes are withheld, allowing the model to predict their class membership based on what it has learned from the training set. Well-known classification schemes include decision trees and support vector machines. As this type of algorithm requires explicit class labeling, classification is a form of [supervised learning](https://en.wikipedia.org/wiki/Supervised_learning).\n",
    "\n",
    "Scikit-learn is the _de facto_ official machine learning library in use in the Python ecosystem. As described on [its official website](http://scikit-learn.org/stable/), Scikit-learn is:\n",
    "\n",
    "> * Simple and efficient tools for data mining and data analysis\n",
    "* Accessible to everybody, and reusable in various contexts\n",
    "* Built on NumPy, SciPy, and matplotlib\n",
    "* Open source, commercially usable - BSD license\n",
    "\n",
    "![Scikit-learn](./img/plot_classifier_comparison.jpg)\n",
    "\n",
    "This tutorial is meant to serve as a demonstration of several machine learning classifiers, and { is inspired by | references | incoporates techniques from } the following excellent works:\n",
    "\n",
    "* Randal Olson's [An Example Machine Learning Notebook](http://nbviewer.ipython.org/github/rhiever/Data-Analysis-and-Machine-Learning-Projects/blob/master/example-data-science-notebook/Example%20Machine%20Learning%20Notebook.ipynb)\n",
    "* Analytics Vidhya's [Common Machine Learning Algorithms Cheat Sheet](http://www.analyticsvidhya.com/blog/2015/09/full-cheatsheet-machine-learning-algorithms/)\n",
    "* Scikit-learn's official [Cross-validation Documentation](http://scikit-learn.org/stable/modules/cross_validation.html)\n",
    "* Scikit-learn's official [Iris Dataset Documentation](http://scikit-learn.org/stable/auto_examples/datasets/plot_iris_dataset.html)\n",
    "* Likely includes influence of the various referenced tutorials included in this [KDnuggets Python Machine Learning](http://www.kdnuggets.com/2015/11/seven-steps-machine-learning-python.html) article I recently wrote\n",
    "\n",
    "We will use the well-known [Iris](https://archive.ics.uci.edu/ml/datasets/Iris) and [Digits](http://archive.ics.uci.edu/ml/datasets/Pen-Based+Recognition+of+Handwritten+Digits) datasets to build models with the following machine learning [classification](https://en.wikipedia.org/wiki/Statistical_classification) algorithms:\n",
    "\n",
    "* [Logistic Regression](https://en.wikipedia.org/wiki/Logistic_regression)\n",
    "* [Decision Tree](https://en.wikipedia.org/wiki/Decision_tree)\n",
    "* [Support Vector Machine](https://en.wikipedia.org/wiki/Support_vector_machine)\n",
    "* [Naive Bayes](https://en.wikipedia.org/wiki/Naive_Bayes_classifier)\n",
    "* [k-nearest Neighbors](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)\n",
    "* [Random Forests](https://en.wikipedia.org/wiki/Random_forest)\n",
    "\n",
    "We also use different strategies for evaluating models:\n",
    "\n",
    "* [Separate testing and training datasets](https://en.wikipedia.org/wiki/Test_set)\n",
    "* [k-fold Cross-validation](https://en.wikipedia.org/wiki/Cross-validation_(statistics)\n",
    "\n",
    "Some simple data investigation methods and tools will be undertaken as well, including:\n",
    "\n",
    "* Plotting data with [Matplotlib](http://matplotlib.org/)\n",
    "* Building and data via [Pandas](http://pandas.pydata.org/) dataframes\n",
    "* Constructing and operating on multi-dimensional arrays and matrices with [Numpy](http://www.numpy.org/)\n",
    "\n",
    "This tutorial is brief, non-verbose, and to the point. Please [alert me](https://twitter.com/mattmayo13) if you find inaccuracies. Also, if you find it at all useful, and believe it to be worth doing so, please feel free to share it far and wide."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Investigating and Visualizing the Data\n",
    "\n",
    "Investigating data is a principal component of machine learning tasks, and there are numerous methods for pursuing such investigation depending on what our goals are. There are numerous resources which devote more energy to data investigaion (such as Randal Olson's [An Example Machine Learning Notebook](http://nbviewer.ipython.org/github/rhiever/Data-Analysis-and-Machine-Learning-Projects/blob/master/example-data-science-notebook/Example%20Machine%20Learning%20Notebook.ipynb)), and as this tutorial is focused on demonstrating various machine learning classifiers, as opposed to constructing end-to-end machine learning pipelines, we will devote comparatively less time to such tasks.\n",
    "\n",
    "First we must import the necessary libraries (they must reside on your computer) and load the required dataset.  We will then have a quick look at the data structure using the Pandas library. Finally, we look at a few simple visualizations of the data, which are often suitable enough to gain very quick insight and understanding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Import pandas for building dataframes\n",
    "import pandas as pd\n",
    "\n",
    "# Import numpy\n",
    "import numpy as np\n",
    "\n",
    "# Import matplotlib for graphs, set inline\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# Import datasets for use\n",
    "from sklearn import datasets\n",
    "\n",
    "# We will use the iris & digits datasets\n",
    "iris = datasets.load_iris()\n",
    "digits = datasets.load_digits()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploring the Iris Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)  \\\n",
       "0                5.1               3.5                1.4               0.2   \n",
       "1                4.9               3.0                1.4               0.2   \n",
       "2                4.7               3.2                1.3               0.2   \n",
       "3                4.6               3.1                1.5               0.2   \n",
       "4                5.0               3.6                1.4               0.2   \n",
       "\n",
       "   class  \n",
       "0      0  \n",
       "1      0  \n",
       "2      0  \n",
       "3      0  \n",
       "4      0  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load iris dataset into a dataframe for exploration\n",
    "iris_df = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "iris_df['class'] = iris.target\n",
    "\n",
    "# Output head of iris dataframe for instance inspection\n",
    "iris_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.843333</td>\n",
       "      <td>3.054000</td>\n",
       "      <td>3.758667</td>\n",
       "      <td>1.198667</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.828066</td>\n",
       "      <td>0.433594</td>\n",
       "      <td>1.764420</td>\n",
       "      <td>0.763161</td>\n",
       "      <td>0.819232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>4.300000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.100000</td>\n",
       "      <td>2.800000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.300000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>5.800000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.350000</td>\n",
       "      <td>1.300000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>6.400000</td>\n",
       "      <td>3.300000</td>\n",
       "      <td>5.100000</td>\n",
       "      <td>1.800000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>7.900000</td>\n",
       "      <td>4.400000</td>\n",
       "      <td>6.900000</td>\n",
       "      <td>2.500000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       sepal length (cm)  sepal width (cm)  petal length (cm)  \\\n",
       "count         150.000000        150.000000         150.000000   \n",
       "mean            5.843333          3.054000           3.758667   \n",
       "std             0.828066          0.433594           1.764420   \n",
       "min             4.300000          2.000000           1.000000   \n",
       "25%             5.100000          2.800000           1.600000   \n",
       "50%             5.800000          3.000000           4.350000   \n",
       "75%             6.400000          3.300000           5.100000   \n",
       "max             7.900000          4.400000           6.900000   \n",
       "\n",
       "       petal width (cm)       class  \n",
       "count        150.000000  150.000000  \n",
       "mean           1.198667    1.000000  \n",
       "std            0.763161    0.819232  \n",
       "min            0.100000    0.000000  \n",
       "25%            0.300000    0.000000  \n",
       "50%            1.300000    1.000000  \n",
       "75%            1.800000    2.000000  \n",
       "max            2.500000    2.000000  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display a description of the iris dataset as summary\n",
    "iris_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f16632320d0>"
      ]
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     "execution_count": 218,
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     "output_type": "execute_result"
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     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1662b9dbd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sepal length histogram\n",
    "iris_df['sepal length (cm)'].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1661968ad0>"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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J9XRYyl1AQVLuAopBbjzGWtRX+10uERG2d/yean19Xaurq5KklZUVra2taTAYSBp/Abs6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f16619718d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sepal width histogram\n",
    "iris_df['sepal width (cm)'].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f1662b11e50>"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f16628d2390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Petal length histogram\n",
    "iris_df['petal length (cm)'].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f166197b110>"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f16680ce810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Petal width histogram\n",
    "iris_df['petal width (cm)'].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f166a396510>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f166a2a1d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dataset boxplot\n",
    "iris_df.plot(kind='box', vert=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f166a35db50>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/2Y4+ISju6WHr6NGcuWULCBEhxvZAIMLNoV1wwm6Yf3V3q4JqYOA6I/NMJvVv\nGaXkCozs6ooYU4s2IiUIrO7Hwn6ns5NZjY083tQUs4jtcLkiItSChN7LA0UXbB2do5BeRXzDfuhw\n7Qytm2SVJl0bIgv7C0LisNpux6yN0WdvmdJ9JSAE5WYzQYOBvrQ0xkd1L3cp4YPhRUbrLtmtLBJ7\nohaP/hrqLjSbI/6maqUA2QhFhOOdq3ULCWBjAjfGNw4HP1Jq+UiE3DRaaqP8/omut6/ogq2jcxQS\nFqrtiuXX5PFgJORe6FBEb01vb4QVGM5m9GlcEZtdrhjLOzp6YrA1sgVQ1dFBUjDI7pIS1Y/dG7W5\nGF5kwu4Sg+Y5S5Sg9pdi/mRzc4TAVbe10TxiBAVKE+B4Ahq9GemW5bjXuGjLFtXSlwktJL/WLECN\nfX0xOSABIdh2gH5sXbB1dI5Cwu6EsO96j9eLTOgLH/bLLunpifDlhv3H2todLV5vTJSGKco/e9uu\nXUxct67f+fQo55RaLKT6/ST7/Vyg+LHDWYfhzcWwe0FbXS8smu6oxaMtQehdQJZZ73BEuFyOaW2l\ntbCQfGWhaooj2NGbkUbgT4plrsWs8XWH5/q/GsFu1lQHDJMEzNeUcNBi8/sH1axBF+xvkf1pxRXN\nM888w+23357w9aqqKpYuXZrw9ZkzZzJ//vxBX8/r9TJx4kS18NRQ8dFHH3HdddcN6ZjfZcLCE/ZZ\ntynhagZC3WN8sqzW6gAosFrxhtPPNbHIrmCQaPs5OvNwcU9PwqJQNS4XvYEATcqYBXY7GR4Po00m\npm3disTeBSC8oNR5PKrVXdHRgQS0e72h7Muo8U0JRO6lOAXZxra1ETAaQ4ItSXHnHL0ZGQQ+iCrW\n5lMibqLRWudtPl/MMQES+7FP3biR7w0iVvuwEGy9Rdj+M2vWLF555ZVBXWPOnDkxnWH2dQ7z5s1j\nxowZERX2hoLLLruM7du3qw0hdA6MsLUatkzDfugAsMnp5J3OTvXLf0xLC8++9JIq8iZNzY94kc7u\nqHRyk88X81yYaZs2cdLXX9OsFH7KdzjIdrsp7ekhaDCQFAjQpbEuDYQs3/C8N955J2leLyafT22i\nqyWRVfqHtraYuY9qb6fAbiff4UAWIqY+d3SDhTANfX0Rbp9NDkfckheCUN1tSFxhsDGOe6Wxr4+6\nvj52DsLH3W/X9EPKF18cvLHPPvvgja3hu9Ai7OWXX+53gTgQrr/+eubNm8cf//jHgzL+d4mwvISt\naK0fereIzjVQAAAgAElEQVTHw2uaELPqtjYK7XZ1k6/L51MFKez31n5KtZEcGzVuB1mWMRj22oA+\nWcYaCGANBHixrU21sNW6JJmZJAcCdPl8qj9ZEHLftHg8GIRgeG8v6X19dPv9bHA4MBJpBcfLgrT5\n/TH+6WS/nzKLBYTAKMsQDMbUE0l0lyCA//T0cGlBAQBfKaVao5coA6G621elpSWsfOgTAp8sk6J5\nn+6rq0Oi/8qF2mvoaDhcWoRVVlayUfHxvfXWWxgMBrXDzPz587nyyiuBWKv5jTfeoLKykoKCAp56\n6in1+U8//ZRnnnmGv//972RlZXHiiSeqrzU1NXHmmWeSnZ3NhRdeiCVBlbKWlhZ2797NaZr6Cn19\nffz85z+nqqqK3Nxcpk+fjtfrpampCYPBwGuvvUZFRQXDhw/nL3/5C+vXr2fSpEnk5eVx7733Row/\nc+ZMPv7440G9PzqJ0VqK4Sa33qgQuXUaoR3V0UGhzaYKdndUVT0DoRjm25RmyIK9Lpe3OjvVLMK6\nKJH80GxWx1lqs2GUZSQhyFC+T660NFL9fix+P00ejyqCJp+Pdp8vJKxApsuF2e9nu8sVczfoj2Pw\nPNPSos4pTGVnJx35+aQGAlizshjW1xdj7TZElX/V/v3/p/E9b3Y6Ex63QYlzdyXYiJWAL6xW9XFA\nlvmkpycUHcPeDeFE6IIdh8OhRdjMmTPVkqXLly9nzJgxLF++XH08c+bMmHN27NjBT3/6U9566y3a\n29vp6elRa19fdNFFPProo1x33XU4HA61q4sQgrfffpvXXnuNrq4ufD6futhEs3XrVkaPHh1hRT34\n4INs2rSJNWvW0NPTw29/+9uIL9W6deuor69nwYIF3H///Tz99NN8/vnnbN++nXfffZcVmm7d48eP\np6mpKWGzBJ3BoU0xtweDyFE+V5lIy7S6rY1st1u97Y+ORRbApIYGnn3pJbUGSDgB5zOrlSAhIYkO\ngXu/u1sVGCOQ6vXSk52tip0nNZU0r5eeQIAWjd+8UxHsFMVKzXW56PH7qfN4IhJtUOYW3drswziJ\nMWPa2zEpXY9smZkU2mwxDRualUXjjg8/ZIxmozEILNNkiO7U1F/RIhOquw2xm5dhjFFjPd3SEhFX\nPlCiji7YURwuLcJmzJihCvSXX37JrFmz1McrVqyIW2nvH//4B5dddhlnnnkmKSkp/O///m+EuAoh\nYlwwkiTx4x//mOrqatLS0rjmmmsG3Q5MlmVeffVVXnjhBUpKSjAYDJx++umkpKSoxzz++OOkpKRw\n/vnnk5WVxQ033EBBQQGlpaVMnz49oh1YeGy9HdiBoQ278wSDMb5aA0RYoNXt7QzzeNTPRvTtvEzI\nCs92u8lxuTASqs8Be6NQDMSmrH+pSQkPApXt7diGDVNf9yUlkeHxYPX7I4ouWQMBun0+UpV5F9jt\n9AaDNPX1xfUx74hKnonX/qu6rQ23Ui2vNyODUouFAJEW7R5lDrf95z9csH59xPn2YFCtK9KcIJRQ\nRqm7HWdzNEwQWK/5/v+xtVU9Nrwh3B+6YMfhcGgRdtZZZ7Fy5Uo6OjoIBoNcffXVrFq1iubmZux2\nO5MnT445J7odWEZGBsOHDx/wWtoej/vSDsxsNuPxeIasHVh4bL0d2IHRpvFBBwgJafQtvNYCrTKZ\nGKYRQ1sgECM4o5XPeGVHB0FgrcPBWrtdjSwRQF2UcEYvFCU9PTgzMvbOwWAgs68PezBIh8+nXt8d\nDNLt96uuk0KbDbcs0xnHLxyd7dji8cR1k4xrbcWgCG5fWhqFSiz2vzTfRZPXC5JEcU8Pk3bvjjhf\nApYoroz+6nObfL5+e1AKzXzdgQBmbb0XQhvC/aELdhwOhxZh1dXVZGRk8Mc//pEZM2aQlZVFcXEx\n8+bNY/r06XHPKS0tZc+ePepjt9sd4Y8+0IiUSZMm0djYqN46FxQUkJaWNmTtwGpqaqiqqiIzM3NI\nxttXegYoJHSk0O7zRXyx12v6GUJkbQ6EoKqjg56sLIQkIcsyvYEAZ3/9NVdrAgGOUVwElUo4pwE4\nf8sW1VIPEpkB+U1UDDSELGWP5u7LIMtkud3YAgG6/X51EfEpzXmHKcJWajbj1RSjCpPm9YbCADWC\nrfWpaxnb2kq6sgD4kpIYrsRiL9X4k7v8foQsU9zTw3FR9UGMksSHirh7Erg7AJyBQMjXnvCIvS3P\n3tG4jMLsHiCLVBfsKA6nFmEzZszgT3/6k+r+mDlzZsTjaH7wgx+wcOFCVq1ahc/n45e//GVEOFJx\ncTFNTU0x1x1spEp5eTnV1dWsVeoQGwwGfvzjH/PAAw9gMpkIBoOsWbNG7YSzryxfvpyLL754v849\nUD63Whm+ejXuw7T56r6gjfKQgFV2e8LFutBmw5ucjD0zE0kIeoNBbIEApT09nKEpdTq6vZ3G4mIq\nlDoc4WJR2k+O1qJ+q6srJgStwG4naNwrp5Isk6vEaXf7IjvCWPx+st1uvMnJjOzuJiBEhOU8ffNm\n1tx9N4LIULn/WCxx3RGjTCaG9/ZGzoW9m4QQEtJUjwchSYzTGG0QCpNcabdHlF+NR4DI+uHx8AuB\nJxjkPeW91DJQ6drDJ6zvEIXeDYS2RVh7eztXXHFF3BZhdXV1pKenM336dFVAZ82axb333stDDz3E\n448/zp133smiRYsoKytj+PDh/OpXv+Lll1+OuFZ/Vu+MGTNYsGABZ511lvr42WefVR9HjzFx4kRe\nfPFFbrjhBlwuFw888ECEe+fqq6/mzTffZPjw4YwePZqvv/5aHWOwcwq3A5s6dSoAv/vd75g1axZT\npkzB6XQyefJkFi1aFDNuf+93mAULFvDWW28NeM7B4OfKQvuZzcblSvjWkYq2aa0BpQFtgkV5tMlE\ne0EB3uRkjLJMp89HbzBIXm8vxyt3hBByhTQXFTFKEw4oEWmtazc7l/T0xGzMFdrtSBor2SgEeQ4H\nNcFgTAnVDp+P4xwOWgsKqOzsjBHJWz/9lMrOToJEhuNtcblijr109WqyXC7yFcE2yDKFiq9Yu8iY\n/X5ynU52l5Qwwmql0GqlOy9Pfb3B42GV4kpJZGNLhErY9vfJl4AvbDa+6u2NGWegJP/DQrAPt1jk\nKVOm8PDDD8d97cILL+TCCy+M+9rll1/O5ZdfHvHcBx98EPFYG4L36quv9juPO+64gzvuuEN9fMkl\nlxCMui184oknIh7fdNNN3HTTTepjrVWfn5/PypUrI47/Iir+/eabb+bmm29OOKfbbruNE088kc7O\nToqKikhLS+P3v/89v//97yOOq6qqipmr1l0DRPSB/Oijj5gwYQLHH398wmsfLMw+H98ooVrLjgLB\nNmv8wRIh8UskBKPb2+nJzsYgBMmKT9UVDDK8t1ctzpTs91NstbKnsFCteAexSTUR5VzjJIEUWa0Y\nNN/1pECA4b29uGU5Iuww3F8y3+HAkp1NmeKKCAtlmtfLZV9+SZbbTZLfr2ZKeoJBtehVmOMbGvjr\n3Ll05udTqkRgGINBRigb2z4h6A0EyE5Kwh4IUGC3Y8vKwp2WxsSmJpZpBNsjy2rBrETvZzi0rz/h\nNQKf9vTE7Y/Z39jh13V0Bk1KSgrbt28/KJmOCxYsGNIxB8uDDQ0YCQnQBs1t84Hy33V1MaFjh4Ke\nQEAVU8HerMcfLV5MWlSc7+j2doIGAwGDgeRAAIvfT58sU2izUWaxkON0UtHVRUdeHjlut1qaNB4y\noXC2Fo8nrp+30GYjWWOFp/r9Ib+2LEekdRsArxCMsNnoS01VXRlhsbp0zRrqysvpyM8n1+lUo1r+\nbTZHCFqO08lHjz7KrvLyCJ90SiDAcMXCNoDqm3YGgxRbLPSlpmLLzGRilB/bQKi860BWsKmfBRJC\n/v63u7riiu9A96S6YOt8p5FlmXe6utQNr8GkBw+GhWYzz7e1JSz2czDRRnlobbjfv/giZ0al/o9t\nbycpEEBIkprE4pNlRthsmPLzmdDUxOj2djrz8ymw2foVbIDNDgd/amuLu/FX0NtLumYBS/P5GGG1\n4pXliLjlsGiNUCzifMWqDS9CtyxahD8pCUt2NkVWq7oZ+b4mUQfgnI0baS8oYFpUslqG16suAhKh\nWigQsqDLzWaEEBiDwbiRIk1KEa1EBNlrId/6n/8wLU6pBQERJWujz+8PXbCjOBpbhOkk5g9tbRGb\nWZYh2nS8a9cuIJS6faixxvkbkv1+Cnp7ObW2NuL50SYTmcoiler3Yw0E8CuNBhpKS5nY1MRokwlX\nejojbDbynE41PjoaI7DJ5eKDBB1d8u12hmkWxGEeD0VWK34hCAKnbd/OjYsWqcJcarGQ7vWS4fUi\nKccMt9s5c8sWJjU04Bg2jDIlgqTL5+MTiyXiuqfV1kZEpajX7etT/dlBYJ3yfxQQgtHt7RhlmWy3\nm+M0PvzwsfvCfe+/z6cPPcQ9//ynmnCkZX+6ReqCrXPUMGn9ehYOIsY9jDMQ4KHduyN8sQEhcB6g\naP/bbFZreAzUEeVg4IjjGy1RwjunRlmblUpaukGWSfd6sfn9BIWgwG4nYDQyqbGRMe3tIMsYhaAj\nP5/yqEa+YSRC9bcTdaQZ3ttLtub9yHK7KbFY1OzF8zZs4MpVq1RhLDObSff5sGZlkay8n5evWsXm\n6mqy+/rwJSVR2dGBDIxcsyamrsjpO3aQGef9z3U6VcGG0F2VcdkyZELhi6l+P+Xd3aFIkQPYXyux\nWGgsKeHuDz7ggffe2+9xtOiCrXPUUON2814CMYnH5Vu3xqQ6S4TqXhwIP9m1S701jy72fyhwB4Oc\nuGsXz2uKaJV3d2PKz+fknTvV55L9foqs1pCYKzU+bIFAqIiTLDPM4+G43bupVkQMoCs3l8oEvQll\nQptpcSVOCPIdDvI0dxzZLhdlZrMawVLZ3U2xJm9gZFcX6R4PtmHD1M3O4xsbkZXIIkmWqVD+v/1R\n7cYkWWZyXZ2a8KMlx+Ui2+3GqFnYwueG7zgKFB93kSZOe19I8fnIdruZ2NiINzmZm5XIqQNlQMGW\nJOmvkiR1SpK0VfPcHEmSWiVJ2qT8XDQks9HROQACQvDNIOuQLLJY+MJuj7ktNQLL9uFL2uH1RiTc\nbHM6MWmiNOJZuwcbjywzur2d05RiYRAS7LrycpIDAUoVkavs7MSUn0+SEBiEYJjHQ28wiFAEscRi\nYXxLC6NMJnKV99WZnq4mz0QjA7vitMaCkDh7UlJI1dy9JAlBUjAIkoSkXK9YU0sj3+kkq68Px7Bh\nFCqL6DGtrerGqVHxOUNsxMoxra3YsrIYHufzYBQCe2ZmxOIRpthiIU8pn9pUUsLEKLdImEKrlcl1\ndUyuq4tw84Qp6+6mIy8PA3BcYyMlFgtVQ7CfMZiwvleBPwKva54TwHNCiOf256KHqj61zneHcDTG\nYPsN3lhbi0TsFz0AfL0PfufzNm8mLymJlSedBMDrnZ0kKeNASMTCYWOHCp8QlPT0RAhrmdlMwGhk\n18iRnFpbyweFhYxub6crL4+qzk6SgkEy3W7Vhx80Gik1m3GnpZHrdNKn8QVXRQl2plJjpK2wMHRu\nnDkV2u30ZGVFuEQAfMnJIAQGSaKop0e19iHkuhBCUDdypGrxjm5vVy3jNJ9PdfVEc2pNDU3FxQkX\nF1tmJsN7ezFryiAYgsFQfLZyffuwYUxsauLzk0+OOf/9J56g1GIhKEm40tM58w9/wJ2err4+srsb\nc04OlV1dGIVg26hRXLlyJb+/5pq48xksA1rYQoiVQDyTY79UN1yASP85fH92u92h+uRxfo5bu1Y9\nzvjFF0xUHn9psyF98QXSF1/wlc2mHpO6bBnXbtu2X/O4d+dO+OILMpYvH/DYrYolpbVozT4fr8ex\nat7p7KQ7qsWTll37ECmyx+uNqFIXnTAiASsOcTGroBCUd3dT0tOjWqMju7sxyDLe5GROVyzvK1av\nxqHU9kgKBslyuzF5vSQFg/SlpmIAdpeW4ktKIk/5G5OCwYjkGYAH3n03VMmvHwrsduxxSg4409ND\nZVcJuR/S/H5yHA6SlCzKtEAAfziVXJap7OxU47Iz+/oiLHItU2tqECKx/7k3I0NdBCLmOGwYKcpn\naFhfHz97/301BFDL+JYWMt1uxra10TtsGG89/TSSxode3t0dUTcls6+PH2gqU+4vB+LDvleSpM2S\nJM2XJEmv1nMUYYmqh6wlHIEQLtkZLhS/zGbDQEigtNljfiHidtmIx/tdXbyrCRsL1yd2K1EA/VHj\ndqux1M3KnH7e0MDNO3fyZZRg3ldX1+9YPYPorRfGGQzilmXMyvyiwwKNhIraD8R8k4klA5TWHCwy\nUKFYluq/3d0kBwJk9vVxWk0N5V1dXLt0KZOUOjDJgQDZbjfdfj/JwSBexaLuyc6mrbBQ/TxkeDwx\nPuyL161L6NcOU2C341Kq5WlxpaWF3CKEBLu5qIgyi4VCmw2bIvBCOb/UYsE+bBjDlEUoz+FgRAL3\n1ZSaGnWRiYcrLS1GiEstFsw5Oerj02praSwp4YPHHiNF8/kbbreT4vczQsloPH37dio7O5nzt7+p\nx4S7w4c5vqGBiU1NFO6nTzzM/gr2S8AoYDJgAp49oFnoHFbECwsLE455DXex9gpBh9fLBocDwd7M\nujAyiRulRvM/TU38UuMzbFIamRqBvw7g/2tQulQbCHUHAfhcEer/t22bWlPlzY6OAUP3Agxc0wFC\nUSbhPoR/NZno8flium7LhAreD8Sju3fzRAJ/6b4Q/jsrOztxpqVRpQhpidnMMI+HUe3tTK6r4/E3\n3mDTMcdQqCwmqUpatj0QIMXvxxd24cgyVk1J3fzeXso1i2quw8GJdXX9xmfnOJ18b+3akPsjCk9q\nKil+P8leL+7UVDrz8ii1WMh1OlXr36BkJla3tdGuyUItsNtDHdCj9glSfD4mNDdTHad5bhh/cnKM\nhV1qNquLRJizN25EAl7405/U58a1tNBUUqIuYqmBANlOJzcuXqweU9nZGbGpmRYIsHXMGC5bvTru\nfC5Yty5uzHY0+yXYQoguoQD8H3BqvOPmzJmj/oSL8esc/lgDAfLtdiZoBKS8q4tbPv5YzWDbqFSA\nMxKqkLbd5UImJNhhazicDGEbZJhcm1K4Pkx4HJnYRqjRtCgJDeFiR7IsqwuFNRDgZ/X1PNnUxG07\nd/ZbvAdCX4rBWLtrlIpvAvjAYmFBnOw1mb01o/vD4vfHdGzZH8KLZZHVSl15uSrYxYoIFjgc2IcN\n47rPP+cEzZ1Gms9HrtOJW5ZJ8/kIKEWaJu3eTYnmvS/u6aHMYlFv/8/bsIFNY8dSaLeTHOfO5P5/\n/pOm667j+KYmRsbxJ/uTkkjz+ch0uzHn5OBOS6PUbCbP4cCp+ISNSu2PasX9ECZZlkPNCKKEd9Lu\n3TQXFamWeDwERBSDgpCF7UlNjXjOAIxpa+PqZctU3/b4lhZ6srMjjqvq6KDIaiVD+T8c2dWlNmBQ\nxwoGuSqqNATAuH//m1NmzaL8t7+F115LOGfYz1oikiSVCCHCJs+VQNylYc6cOfszvM63jC0QYITV\nym3/+Q8P3H03ADcsXcoF69bx+iWXALBdqUgmE6qQplrRkqRmcYULvUdbnYnoDQYjwuzCdSEEoaI+\n/dGqyUDb4nJFhOYJ4I/t7QPWaQgT7p7ygxEj+j1uTW8vRkIW+TdOJznGePl9iRuyqq97vQTp/85m\nsISL8Bfa7ewpLGSMyQQitAkZfmebSkqoNxo5V2lBB5Du9ZLncOAXQi1DCqFIjXzNHUK6348pP59j\nm5vZMWoUl65dS19yMp15eZSZzTSVlETM58cLF9IyYgRnbd4cd76yJJHu9ZLm82HLykKWJNU1ERbP\ncAr7Ma2tEPVZMufkUGKx0Kl0kwGYun07Hfn5HBtVcU+LIRiM2ZDUbnhqKbZaaSsoYHR7O7vLypjQ\n0hIzD6MQNBUXc2xLCxvGjaPMbI4R7GNaW0kKBpFkGaG4S8q7ulj65ps0TJzIhOZm3r3pJoTGtRIz\n74SvKEiS9A6wGhgnSdIeSZJ+DMyVJGmLJEmbgRnAfw80js6Rgz0QYJjHwxVffql+gH+wYgXVbW2q\n4NW73Wofuo2KZQahTeVwbYcWxQcdrjERjbb0qyzLBIQIpe0qAqfNQOyT5X773WkbqjZ7PLzR0RHX\n2k3EpPp6Vt99NwZls2swVvEWp1MVwT5ZZnWc6msQv1Gslo97etR+hvtSk/tLm43cKIut3edDEoI0\nn4/kYJDRJhP5vb14UlLIUMY+dccOztaINYTStfOV6JhhHk/EBlo0NZWV/OkPfwAhOG/9eio7O+nO\nzY0RwIy+Pqrb2xkXVfRLiyRCFftKLRbcaWkYg0FGdneT53TiVVwo6T4f+b29HNPaqsaDh7FnZsZs\nPF6xalVMzZRoKjs7uWr58oiszfDGbDx2l5SoWaITm5rU5gpauvPy1DDAUrM5xkdeaLdjy8xkglJU\nC+Cvv/kNO0eO5KytW+nNyIipXxLNYKJErhdClAohUoQQI4UQfxVC3CSEmCSEOEEIcYUQIn7sjM4R\nSa8i2KUWC8fv3k2xxUJ1ayslPT0gQpmATR6PGr5l09RFlgGrYhm3KgXmAbZFWcgBWSZ5xQrV7RF+\n3UBoA7NHE8sMIdfL/H42trRuF0cwyOc226BTiYstFj6aPZtJDQ2MbWsjyMCF5CEUTRK+hhFiKsVl\nO52gLEKt/Yy33GpV/e9L9mFT6mf19RGtqyBkzScHApizs8lyu6ns6KDMbKZLU3Uu3e+P+eJneDyq\nTzfT7e43BOysb76hyGrlmXnzCBiNVHV20jtsWMzG44n19dSXlUXEXkcjCcEtixYxpbaWoCSF4sQV\n942sWKGZbjf5vb2Mbm+P2Uj0pKZGhPblOJ2csnNnTB2QaEZ1dtJUXBxydSiUmc2kJVgwAwYDpytZ\nomP37FHjwrXIQnB8YyPJSqXBEXGOaS4u5oxt2wDIcrk4fccOTlPGbS4p4WxNy7x46JmOOjH0KiFe\nG445hh+sXMn/W7WKrdXV2LKyMAhBfV9fRBuksNhAyP1gU6ygdqWQvoHY1keNHg8y8LHyZVujFPgx\nKL9viOpMHWRvVTUIldJcpbFgtFasADU1fCDSvF4+nD2buvJyNo4bx0lKDRDTIDZKtVmMYf95mGS/\nn+3/9V+csnOnugglYoPTGWpkK0ksH6CnXxib36+GE2p7DHb6fKp7odBmo6KrizKzOWLjMB7Jsqxa\nm9lut9qxPB5JQoAQ/OLdd2koK1PvoiqjNh6n1NZGRF3EwxgMku90UmY2YwgGyezro0TxYYet/ByX\ni+G9vYwymSiN2suQFXdPmEvWrGHr6NH9+q+13PfPf6q/l1gsal2VaHJdLk6trSXV56PMbI67yZrh\n9XK8kiTTnZuLMY57xRAMMmPLFgDO3rSJHVVV6lxTfD7OTtBPVT1/UH+VzncKhyLYxmCQK1au5KoV\nK0jxekM1HQIBGvr6Ihq1hsP5kv1+yru6sCmWZofPB5KEgVCNCS3htk5hIfvG6cQgSQQJuRq2OJ0x\nH06tH/u/6+s5T/Ph1hbANzL4JIGn5s/Hm5zMORs3EjAYOFnZiBvMRqlDc4wgMgnnypUrKTebOaGh\nAYMksaaf0L6w4AaEGHSxqF/s3q2+71r3TbffT7rHQ29GBkVWKzlOJ9VtbfRFbabFQxJ7E1aMwf7v\nTya0tLB80iQ1lTxJcb9oOWPHjhg/bjTJwSB5DgflFgvJwSC5TifFPT3kRwl2Vl8f3uRkcqJcVUZZ\njqhtctXKlYMuqnTKzp0U9fRw8s6dZLrdlJrNETVGtIxub+f43bs5trmZPSNGkBxnQSuyWhnf3Ex5\ndzfdCRaqEotFtagvWbs2IiFpTHs7ZylinghdsHVicAYC5LhcTGpooFT5gB2/ezeOjAzSvV72eL0R\nFm1Q+blo3TruWLhQFTKz348QoRoP0QWBwi6HcIumWrdb9WHX9fWpRZO+v3y56kf3yDLtynn/NJvx\nKO4Zt6b+c5jBfLBPqK/nxsWLGdfSgkSoGNEpSq0NbxzrSItPlmM6qmi571//YmtVFZN27yYgBPNM\nJjU+XIssy7g072X9ICNF3lSa4RqIdN/0+P1kud14lMSXtoKC0C34AH8P7F3kcp1OUgaxYJ3zzTeh\nDThC1mW0S+Tk2tqEmYhhwuGERT09ZHi9FNpsFFutFPT2qhaqUQhsmZlqJqWWFKWdGYTuls7euJFj\nNT7i/jAKQX1ZGW8/+SQt115LbWVlXDcGQI7bjWn4cH6wYkXEBqeWkV1dFNrtjG9piYhm0TKmvZ0C\nu50RPT1csH49ZZrFpthqjQkrjEYXbJ0Yevv6SPf5SPf72TZqFFtHjyZTiZPN7Otjj9cb09IJ4KS6\nOoosFjUqxOL3M6a5mQy3OyZlvEW5DQw/r02u6fL72e3xkOTz8f6cOepmlhH4v44OzD4fXUpyz0cW\nS0zT0/AC0h+GYJD5v/kNNRUVaixyZWcnxzc0qH5nWz/W4Xql3kQ8jm9oYJTJhDstTS3RKYRg8tdf\n44myXNdGWdT9WfYPNzQwfu1aRq1Zoy4oEntj4iHUvCDH6SSolH/ozs1l2vbtA1rMsPcOYXhvb8zm\n3kDkORwRlm6+3a66MfojzeslRxHsbJeLdL8fd2oqo0ymiGYH1szMuG6dDI+HImVROHfjRurLyijY\nh9ICJ+/ahSk/H29yMjM2b47rxgjTVljIj5YswZcgGsgoBI3FxVzw9ddqWGQ0BkKbtjcvWkRKIEB1\nVHGq5gEag+iCrRODw+VSv+ATmppUKyBgNJLtclGbIIJiys6dlFksarsni9/P2d98w/G7d6ttnMK0\nKxuSLllGluWIPoR9sswej0fdZQ8nFMjAR2Yzz7W2YiT04V1stVIzwCZZPO5RWrdN1yQrFCpdvSs7\nO5EIiXIiViu9/eJx37/+RW1FBWVmM+MVCzRIaG9gepSP8hOLJaLYf5C9UTJantuzh9/s2cPOvj6a\nNJl7fc0AACAASURBVI1gBdCmWexsgQDDHQ7VB+1OS6Oiq2tQAhwWqwKbbcAoi2iKe3pCgq2MMWXn\nTnZWVAwoMMM8HrJdLoqsVjUuuis3l/HNzRFzdmRkxI2fz3U6KbJaSfb7+em//63Gbg+WHLebGVu2\nUDyIzV5Jlqnq7Oz37qM7L4/zNm6MSebR4klJ4aEFC9g5cmTM53ag910XbJ0YXB6P+oUvstnUzSRJ\nlsnv7WWHy4UB+OVrr3GCktoMqC4UvyZhJlyEKDpzsNPvV32NGxyOmFjtNmVzB2C6sqsuCEWTvK00\nXw0Ca3t7qVMqxD0zbx5j+wkhC1Pe1cXjr79ObtTGJkBTaSkn7doV2ijtR7ATVQUc1tfHVcuWcdzu\n3ZSZzWS53eQox8qECktpLfc1vb0RQmQAFkWJxyKLhQeVJsHRBCFiMbQFAhTYbOr/X9gPHF10KR7h\nc0bYbHHD1vpjmNeLOy1NTRU/bceOQYlnllIPJMXvJ0fZo7BlZYW602jm0JeaGrdxQoHdTonFwrKf\n/Yxcp5NToho0DCXhKJp4Vf7CCCEY3tvbr6jnOp0U9PbGjUiZMsD8dcHWiaHP54sbh2sQoT57JiX6\n46oVK7hh6VIgVF8hS4nNDirnOoJBShUr0xd1qxmOmzYC75nNMSF8fbLMqPZ2aioq1DAoAI8QES6A\nJo+HRiWF/fqlS7l81aoB/74/P/88m6urQ0klUXiSkjiprg4JqOnHn1zrdhMkVPjoRk2t42lbt1Jf\nVsYIux2JUPyutkSnEXhKk9Cx3e2O2CQzSBIro/yo39++vd+/p0uzAJj9fio7O9XNvrCVGq+AUTRB\no1FtUJsoWqI/TPn5VCiL+9SaGjIGERqZ5XKR5vfTmZenLp5uZYNUW7Z0QlMTp2rKxYYZpmyG96Wl\ncfr27WQexPrj1W1tmLOz+03DDy90/b1/x+zZQ09Wlnr3pSXeZqYWXbB1YvAFg3FdDMmBAMU9PXiF\nQCK0yXLhunUAnFhXR315ObIkqeLrVpIgJjY2IoiszxEusCQD/+zuRgJ+vmABD7/9tnrtiU1NdObl\nMaatjSzF+gq7QsL0yTLNHg8iGKTcbOZ8TULIeV9/TceVV/L7F1/khPp6Kjo6+NHixYxvaeHMBLvx\nwzwepuzcSYDYjVItYR/8xWvXctOSJerz53zzTcSGU09OTkQyRBD4m7I51+H1qlmQv3vpJW79+ONQ\npEiU9e6W5X7T6Xs076szGGRsa6sqllluN36jMaZuRjwCRiPJgQBFVut+CbY1O5vKzk6G9fUxpaZm\nwIJQEAoR7M3IiEj1Dv+t2ruCXJcrFE4Yh0KrlXM3bjzoYpYaCJDtcpHdz3sTTuLJ78cKH+b1kul2\n91ucKhGHrkivzhGDP8Eqn+bzqQXjjUqCRkVXF0U9PZy0axe9GRlkO53IkoQsy/gCAQrs9lCIFqH6\nIzOVBI5wESlBKMrBAJy5fTuSEGr0xYSWFlL8fnZWVHBaTQ2fnXJKTMiWBGx2uch3OLANG8bpygZb\n0GjkR0uXUlNZyfG7d/P+L39JSiBAwGjEkZ6eMJmjvLtbtRJb+rEQrcqCM7GxkWy3mzSvF09qKuds\n3EiSZmwpGGRSVFGnbr+fBrebH2zfrmY4nrtxIyUWC/MvuYTdGkHobw5hnBp/qU8IdU4Qyt77ety4\nmNZg8ZAliVEmE/l2e7+bb4nwG41UdHZy3z//yfZRowYMUQvTm5ER4T4xyjKyJJE1yPZqiYT8YJAy\nwObtyK4uvj7mmAhX4f6MkwhdsHViSPRRyuzro0Kxmobb7bQVFNA5fDgXrF/PqTt3kuLzEUhOxijL\ndPh8BGWZDI+HbKXuyGaXSxVsrc86/HU7trl5b/snoKKrizSvF3NuLtO2beOzU06JG77nCAYZ3d1N\nQ1kZ2S4XJ9bVsWnsWL63Zg2+5GR1kRkMpRYLPVlZ5PX2YtFkB2rZ6HAQBAqsVlL9fmorKpixeTOr\njjuOY5ubIwQ70+OJ6VpiBC7dtk3dvE31+ZioZMhBZMbkeiWhKO4SKgTjWlpoqKoC9hbLGtfaqh6S\n63INSqzD3PnRRwPelifCoHQav/irr9RKe4PBkZGBX9PgIcXvx56RQd4A9WMORwzAKUry1cEaX0cn\nhng1FXJcLtXvW2o2Y8nJQQjBpV99xQn19RRbrXiTk0kJBGjzehGShC0zkxE2GwYhqNV8Af3RVlEg\nQGVHB1UdHWo9j5FdXRTabAzr60torYWlraqjA1d6Ou0FBZyzaRNnbNtGd17ePok1hBaK3WVlHNvU\nhDuBFfSqyUQSoapwDaWl2IcN4+K1a5m2bRu1FRWkaQQ73GYres7aSJvJ9fU0lpQw2mQi1esN9SdU\n3v9tygZvPC5Yv54PHntMLZj1dW8vBiFIDQTI2g+XhkGWKTWb49atHgxpfj8/WrKE2srKuPsDiXCn\npUV83jI9nn0S/O8SuoWtE4OAuLvc+b29ajbcqI4O+lJTGdfSEqqfEAiQ5vXSUlREms8XKndqMCAA\nS3Y2qX19NCi393KUT1YiZNnuGTGClECA0SYTLSNGkO9wkKTUZ06SZQzBIHKC+NYJzc0gy2T4fJy7\ncSNlZjOdeXkDFtOJhyMjgxMaGlg9aRIBWSbJECmZn1qtBIATGhroHTaMEouFUosFb3IyvVFCU2qx\n4MjIINfhwJYgPfzUmhpaCwvxG40cv3s3Xx97LM1eL6PS09nV15fQf33/P//JGJMJIQQBWWaLy0Wq\n348lO5vSARJWEhEuwrQ/ZCvx8OX9bMrFw5eUFJEKP6atjU1jx6oNdnX2olvYOjEIgyFuCFWyLIe+\nWEIwobkZgyxTZrHQnZNDQ1kZSUIgKW6QbS4XSf+fvfMOj+ss0/7vzEij3nu1JFe5O3F6wE5CsqF3\nyLIQYAudwPLtspQNJCy7lM3yhQW+JRAIKUsgCZBCQppjxzXulm0Vq2tGbTQjaao0/Xx/PNM1M6ou\nBN3X5cvS6Mw5Z86c87zPez/3c78+H/70dEyFhZRaLOEiXqjQ9s0HHghn01d0dDBaUsJwaSnNwfbe\n0aIitKpKicOBqbCQrSl4wS29vWR4vaw2GLiqrY137t8/78ARgtbnY0uQxkhk69oX/ByXdXeT5vOx\nVq+n2Gbjg7t3zyg2KUBfVVXKgeOa9nbSvV7Gioq4vKsLDZFVaqJNtqLRMDLCVe3tWHJz0agqPdPT\nnJueJmd6molZfEOSQRMIUD0+HtMuPR+sNRg43dhI0xyKjdEocDhojro+2R4P182ijPlLxXLAXsYM\n+DWaGA1sNKy5udSPjrKpvz/ciTZYXs54sMqvqCo5wdbyTI8Hn0aDNTeXOpMpLOXrnp5GEwhw10MP\nhVvBt3V349VomNbpWKfXi2VnFIesr6jgnx57LOk5r9XrKXQ4KHE4GC4tRVUUVqdYcSQVcqenaR4Y\nQMvMBXmP2WzhALqpt5fi4EIObY2NlFksrEvQFj2Rn8/OFKY+2zs6qJyYQBMIsD2oAQ+tUmNI8j18\n9qmnaFm1itHiYnTBxQ96p6cpsNtj1hKcD7TBgO1ZYMDWqirbkujFU2G9Xj+v7sS/ZCxTIsuYAZ9W\nS04SdYI1J4c6s5laozEc1K9obw9bYWoDAQqcTnpdLvFVVlU8aWmsGhxk/5YtgKzVGKJc3nLkCEfW\nr2dzb294pZONAwOYCguxRykHtnd04NbpWKvXc66+nrcdPMhbjhzhM1/8IiBt5SHqILSMVPzq3nNF\ntdmMgmTHZ+OkV78cHSUNUIPyudBEPt3j4WxjI1cEB6BoNAwPc0dfHwc2bmTPtm0xfyu026mcmCDb\n5cKVkcFlnZ0xq9REL2pwz//8D6uGhrj/LW/ho88/z1RGBkNlZWS73fS4XBjcbiosFlwLDLhpfj8Z\nXm/StuplXHwsZ9jLmAFvWlrSzjhnZiZlFgt1JlO4lTjP5Qq7qOl8PgodDkY8HvKmplACAbR+P816\nfdgXesDlItvlYlqn482HDwOiECmzWChwOlk3MDDDDD9/epozTU3c/atfsbWri19+73t8+MUXyXK5\nKAy2Yod0rW9oaeGNs9hUpkLl5CQ5QS+THw0Po+zZQ8arr/Kn8XFeDK6KvsZgYLS4ONyocU1b2ww1\nSAiNRiNDpaX85lvfYlWUggPEMe5cXR1aVaUxZPbv94fpo+lg4fP606f56127KLTb+c7999NZV8eK\nsTHcOh35Tid6l4txr5fq8fGw0ma+CA2iF04kt4z5YjnDXsYMeNLSwu3UM/6Wni6radhsaBMUJjO8\nXoptNia9XiqdTtICARRVpdFoDPtCD7rd5DmdnFizJrxAQq3JhNbvx5adjVZVaVqxIryadghXtLfj\nysjgjS0tdNXWkuHzsaOlhbHCQgbLysIreSxU4xqCAvRXVrKpu5uj69fL51ZV3nLmTLipZ3Nvrywb\nFVRDKBBe0SURtnV3s3vLFu6/5x523ntv+PUrOzrCjTa5bjddNTXUmkyMZGTgC65Mn+7x8PN77mGg\nvDzspRyCirRKD7ndTPn9orJZoCwv1B2pXEBd8zLmh+UMexkxcPn9+DWasK/DDKgq27q7MRYWJmxY\nCK1cMhX0HdF5veROT1NtNqNRFA7bbIwGl3xyp6dztrGRzz75JIayMnR+PyV2OwFFYXtHx4zW5jyX\ni7aGBtobGri2rQ1bdjZvPXyYppERxmcxyp8vxgsKEq4JGArYW7u7500dXNPayqaenpjFaK9pa4sx\n/BkuLWVzTw92vz8s/fvqo48ymZ/P1Qlas7V+P+WTk4x4PPiAZr1+Ts58iRDytlgO2JculgP2MmIw\n4fWS4fUm7QTUBAJc3tkZs+RUNPKmpii3WFBBDHw8Hlmzz2zGp6qccToxejxUWCxoAgG8Wi2ffuop\njCUlQNAutLKS9QMDCU12drS0cGOw/bxqfJxbjh6laWQE7xLzrqqqsiFBATGUu27t6SFrDl2I0cj0\n+WhZvZoPvfwyIK5415w9y6qo4qiqqlx39ize4GIGGuDvnnuOsuAyYvFIDxpshTyx1w8MLKitHAjX\nJBaaoS/j/GM5YC8jBhM+H1lud1I7zrRAgI19fUmVCPlTU2HT+vLJSXKmpymfnJRlnAIBuqenMft8\nVJvNpAVXri6x2/FFaZ2tQRP32czv1xgMFDocvOn48QVnlcmQ6fHELJYajTSfjyvb2hZU1Cy2WsV7\nRFX5yqOP0rJqFeVRPh+5LhdXBx3bdlksaFWVislJGpI0omR5PNSNjTHq8aBBmo3m4huSCCHjolTL\ngy3j4mI5YC8jBhNeL9lud1Jf3ozgatzJHulst5vCIJ1SbTaT73SS6fNhy86myG7H7PViC3qQZLnd\nrDAaGQg224Sg+P2YCgrImsXDWQO0NTRw8/HjSVUtC0WZ1cqaJFatO0+dwlBePicP5Xhs6u0ld2qK\nNx0/zsefey5GfwxQZrHQMDKCBthvtZLjdDJSXJzULyNvaorGkRF8qoo26KY420CXDCEKKj3J7GoZ\nFx/LAXsZMZj0+8lxuchKUkALBcb4gmAICpEpdWj1awBjURF1Y2O4VZWpQICVw8OiIgGmdLoYs5wc\ntxtjEsolHunzsA+dD+rGxqg3GmN8QUJ47759Me5y84EG6Kqt5bG77+bU6tVUxQX9GpOJyokJtEEX\nwrKJiaRLUgEU2WysCSpPsqemktYW5gKd3487PX3eq80s48LhdR2w7zUYZl02fhmxsHi95ExPJ/Uy\nDsn95mJwn+XxhIOHNTc3TCG4AgFWGwzhBU+bDYYYhcVlnZ3hQD8b1ur1ODIzF9yKnQwZPh9DpaUx\n/DLIggDvOHBgTtahydAwOkqa3z8juwZxnhspKSEvuJJ6/dhYSm+PIocjfC7FFgtjKYL7XODMzExo\nrL+MSwOv64D9fwcH2Wu1ho10ljE7Jj0ecqenk1IMoSCbbHVpILxMVLTawJ2eLtK94O8NRmNSz2Ct\nqs7ZtKnUbsev0SQtki4GoyUlM4ybtp87hzMzc97t19FYOTKCJhCYkV2HYCwupiLoq7zWYEhZBNQA\nqqJA8Jot1jTJVFCQXCG0jIuO123AnvL5xIAI2LvE0+XXM8yTk2R6PEn9kLM9Hs40NqbkSdNCy1NF\n7UMTCLByZESUDqqKNy1tyW6+gjn6Js8XLp2OH/74x/zrww9TFRxA3rtvH/ry8kXvOyfFDGUqM5Om\n4OKsW3t6wvroZLDl5KD1+1k5NDSn1dFTYe3g4IK4+T8X2HUQWFhf0SWB123A/vHQEFpVJcvj4cEF\ntij/JWLSap216LSpry9lQTAkD4vmuXOmp7msqwsfUtSaXCAHfCFx04kTODMzueHkSVo//nGe/trX\nuG3XrvCqIucLWp+PTcGuyW1zoIfsQcfAKzs6lguGs+AD74dnV1/ss1g4Xredjr8yGtlx4gSbe3v5\n/Yc/POPvL4yPU5+ZSXPUck7LAIvDQfoiJXJpgQC37doVYyC1wmgMO/1lejwzbEgvVTTr9TTr9dgz\nMylwOOirquKNLS3n9ZhZbresY6mqrB4aCvu0JMO0TsebTpxgS2/vnNZRvJjwK3CsGq5amC/XonGq\nEgYKL86xlwKXRIZ9V18fE0tY6PAFApxzOvnmgw/y0eefZ9DlmsFj/017O7cn6Bz7S4djejqpAmSu\nUAIBfvLDH6JEeVqUW6140tOpMZm4rKsLd3r6Yk/1giLP5eKNZ86ws6XlvD80JTYbzXo9RXY7qqLM\nmmGrikLF5CT1RuOCNdgXCieq4NYPXxy/kslMGM2DoUt/cpcUFz1gBwIB7h4Y4IFFFHHi8bDRSM7U\nFNluNxpVJc3nY0/UjRwIBJjw+TjpcFzUgmQgEOBDra04LqFprNPjWXSnm0ZVZR3HuMDfV1XF9s5O\nbjx5MuGq7MsQ1JhM1JpMrBkcZLCsLGGHYzQ0wQakMquVyiVWyyw1+gvBkgXdixOzLAitwdLDUP6f\nL4l90QP2bosFgONL6If785ER3n7wIF6tFnNhIWv0eh6KGhCO2u3oPB60Xi9/PM98ZCp8uquLR00m\nnjmPD9kxm413nTkz5+2nfT40iyxchboO4/fjSk/n8s5OUYssB+ykyPT5MBUWsqOlZU5cf7rfz+Xn\nzjGaosHmUkF/kI44UnPhj91aBpV2GMq7tK9RKlz0gP1ksPretoSV/r7hYa49e5bt586RNzXFLceO\nsSuq8v2E2czlnZ3sOHWK/46zu7xQOOd08vOhIapNJvYnMBlaKvxNeztPzWNAcAd55sUgJLGLbxfP\ndru54tw5KicmlpszZsFIcHHjuXikZHo8bOntTervcimhpxiqbXC49sIf+0wFrJyA0T/jstVFD9h7\nrVbW6vUYljDTzbZaGaisJD0QYK1ez0dfeIEhtxtPMKvbbTZz44kTfOapp9gfzPAvNG49dYp3HDzI\n7S++yKne3vNyjANWK51BI6CuOQ6I3iXIfEONF/Ha6FqTic09PVROTCzYoOgvBY6sLK4/ezZhp2U8\n8qamyPB6cUQt+HCpoq8IVo3D4YuQYZ8tF+58NPfCH3upcNEDdrfNxud//3s8cyx02Xw+XLNs69Lp\nqA4u4Jk/PY2qKGRPT/OjYDbdNT5OvdFI3dgYfp+PwxewUOMLBLjx1ClsZjOf+/3vGc/Px3iess2P\ndXSgQVQbr85xYPLDrJzpbAgpFeKXGasxm8l0u1ljMCR04ltGBJpAgAyvd04eKaGFGxY7M5oNU0tQ\nJx4ogPFs4ZO9Fzj6tJdCbxHYM8D1Z6qPu6gBe8rnww18YM8epjMymJpDNrH9+HHeMQsna83NZV2U\ncc94QQHXnT3LT4aH8QQCTKenU2S3Y8vJ4bLOTr7Q3c3/DA2F/z04MnJeipGjbjc1hw5xYnCQP371\nq1xx7hzlExN4z4NiYr/FQvf0NFedOcMtR45wJCpAnnU4Yq51IBDgWKhzUVFmbdSYDaH29Zy4LFoB\numtryQ16Zi8jOUKzlLlcp2KbDb9GE/ZVOR/oLoa1n1ucukMF9AXCY9fYJOO9UBjPAneaqEQqHKmz\n7NFc8F30VDYxLuppPTM+TqnVijUnhxKrlX1zuDkH7Hb2peBkJzwevGlpNEdZY+Y7nXzymWfoc7l4\nbGyMQoeDMquVFaOj/OvDD3PMbufzXV3hfx87d47Hgxk6wLDLxZ4l6P76WEcHZq+Xp7/2NVRFoWBq\niq09PYzn5y/5APHtgQE0wKeefZbLz53jTNS1ve7kSf4piob5yfAwV504gS94DosN2KHVavITtDg7\nsrIYz89f9Kowr3eEgvBcnPe0qsp4Xh55C6SZVESfnApnymGwQDjohcKUA1lecGZAjUO5oIXH1nJo\ntAAKlEzDcIqF5f/mPfCbjRfs1OaFix6wr2xvF5Od4WEOzBKwh10ulEAAjcfDoSTbtjocVExMUBEV\nYJsHBth56hRZHg9f6unh8s5OSq1WmkZHWWcwcFl7Ow1DQ7zr1VcJBAJogeej3v+Jzk5uaGlh1yJ5\n9tdsNjZ3dlI1McFVQQ34tq4utIEAXXEPm83n49+T+DHPBe1TU2i8Xt5+4AA1ZjP9weKuJxDA4fWy\nL9j6DPDCyAgB4EGjkYCikLnIgK3z+9mzZUtkqh6FDI8H859Bl+PFxgqjkX2bNs15YGtbsYLGJJ7Z\ns+FoDfzVzN6yGLTLusYcrFvQIQDoK4Tq4ETPh8prdbOTb8+vWppW8tYyKJqWHeV7Ugfs3iJ4aeWl\nKf2bNWArivJLRVGMiqKciXqtWFGUlxRF6VQU5UVFURbUO3RwdJQdLS1s7u1lS3c3J2fhNR8bG2Nj\nby+3Hj3KPUmUFSe6uymzWMiMmvLnuN2cWr2aW197DZPXyw0nT4Zd2Azl5fzhzjs59NnP8u1f/IJn\nvv510txujkSZGx0PBp5bz5yhLy6wfqe/n21Hj7Lt6FE+39mZ9NynfD6sfj/fv+8+TAUFYa+O+rEx\n1hgMvBSnVvmeXs+/9vVhWWDwNHo8vPH0ac7V1eHTapkKZs/Pjo8T0GgYjzJXOtPfT93YGD8dGMCv\n0SxJt1yyBpP1AwMLtib9S0KGz8fOeXRU7jx9mvwFZtgH6oRXThUY2yoU1phhb8PCA1l/IRQHby1T\nDhytTk2wBBR4523QUTrzb5OZ8MT6uR/7TCX4g4ROuj95wPZpwFAAe+svTenfXDLsB4Bb4177CvCS\nqqprgF3B3+eN8akpMj0eihwOasxmOmZpnnmmtZWtPT3ccvQou5LI8ToGBxO6jdUbjXzvvvvQBAIU\n2e1hBcOGvj705eXkO500DQ+T5Xbz83vuoT8qOxwL8okBVeXy48fD9IXL7+fr/f2ccjo55XTyk+Fh\n1h4+jC0BF/+w0Uie08mKsTGubmsLv54eCFA1Ps6+1taY7Z8IDkg/i8qE54pAIIBbVfmHZ5/Fp9FQ\nOT7OdGYmvkCAp0ZGeNOxY0zm5YUpkKn0dO586CHaJyfxabUzuOelRJHDwTVRn38ZFx/7GsCvAWtG\n8m06SlQqHXCoZuGBrL8Q0oLMX3eRZNzOFOUbYw540iQ7jscX36zwibfPnVM/WybFRpDC+mCSnGEo\nD8qd4NRJgfRSw6wBW1XVfUA8gfsO4MHgzw8C70r0Xk8KXnbY5cKVkRF2JUv3+RifxWO522Yj2+Wi\nanycaa02oVTNYLMl9GpeNTyMJS+PX3z/+zFLO1VYLFzT3k6Gz4fO7+fGkyepmJzErap4AgFaHY7w\n6ioBwOLzcU+woHlnf79cQFXl0089xXfuu49ep5O6Q4dmcNJPmExc29rKSHHxjIue43LRE5XRBwIB\nhqemeM/evfxvT8+Mz/Kfej2Nhw7xo8HBhNz3KacTJRDg1iNH2NrdTbnVSrbLxUm7nQP9/bz58GEK\nnE72Wq2Yg74el587R7rPx3BpKQVOJ9+7Ho5XJfwalvE6ggocqoFsj2S9Ifz0cthfH9mmq1gCp74A\nLMntuVOip1jBG0zQfWlQaxf6IRlCnh+tccXJ3Q2wq1FFUVO3mRvy4Y0fh2v+Ho5WSzAGyaKHk3Q7\n9hdClQOazQp7Gub0sS4oFsphV6iqGop6RqAi0UY/Hkru8HLP4CDbOzpYEQyexXY7njTR2tzZ28u1\nwYVWo2HPymL14CArjEaua23l+wmWcBr3esOOZQ9sha++KfLF+DQaPvbCCzPkZvFI8/spcDp5eWKC\nx00mSiwW+m67jb7bbuMrjzzC3f39BAIBfjo8jMbr5cHvfpc7fvc73nDmDPs+9zmmXS6+HnRbC+GI\n1cqHX3qJ1QlmBtkuF84o341dFgvpPh+f+cMf0CeYLTwwOkq/280XurspP3hwxt93TU5SOTHB6VWr\nyHW7KXA4aBoeZp/NxkSQirmio4OnR0Z40mxmzeAgfo2Gd+/bhysjgyKHg19vgv9446XJ4y1jYfjg\n+2ZmlgOFoCqwegLMUX5cTzXDI1vk55E8yPDDeA6sG4fXFtj00l+kMh2VUZdMyQAQwh/XwA+uifyu\nLxD64nRF5D50pcEn3i7NN6sm4XTCyCN4brUEZ2ca1FtgLBiwp9NgOEm3Y38h5LsVVFXl5UuQx150\n0VFVVZUkM5MfJ1hRI4Tf9vfz3r17w+vmNQ0P49HpOGaz8e96PYfjDPLPOhz4tFp2njrFxr4+3rN3\nL39IsP9ppMNudwN8+Wa473I1rPe8oqODtvp66sbGUn6mAqeTTT09PDsxwa7JSa5tbaW/shKt3887\n9+8n3W7nva2tOPx+Hr/rLppGRqgbG+Oa1lamsrL48Q9/yA8MhjDl4PD5cPp81BuNVCcoXDYNDzMV\ntarIfUND3HrkCKqi4NdqORpXYDUND/ODH/+YsokJxn2+8HFCOGq3s9ZggODrtSYTm/r62GexYM/O\nZo1ezwqjkb1dXTzX28u2ri4u7+zkmiAtU2Kx0F8ALzWp4azkhZXwvg+kvGzLuITh0cLv1ktQjMaB\nOlgzDrne2IA9lg17VsjPHaVQH7wF89ywr35h59BfABNR2XmWL9Y5b+8K+FOU9elAAWwyQntpj0No\n1wAAIABJREFUJLzcvw3KpuBoLeR4oCVFwN61UkETEP66M4pWsWXCSJJux94iIKBiyE/NY3/w/Qpf\n+isZEAIK3HkjvOu22G3edRuk3yn/PvKepTG8WmjANiqKUgmgKEoVkDACDvzsZ/zLnXdy1113sWfP\nnvDrDp8Pc5C7DXkfFDoc1JhM3NjSwrr+fjJdLlqjeOSHz53jinPnWKfXo1VVakwm7BrNDFrEr9WS\nazfzwfdBrRXqrISnNmmqSrNez4pZAvbqwUF2tLRwaHycs04n79m3j5VDQ9SZzWR6vdz9wAM8OT7O\nhr4+1un1XNnWRo7bjQLceOIEG/v7ybdYwln2w0YjVePj+JO0GV9/5gxjhYXhwLtnYIDtwc9789Gj\n/DC4ijYIzWTPzuayzk5OfPKTpHu9M4q1rU4nV7W3h5UyxQ4HDaOjvGw00jA6SvXEBDkuF0aPh9Mj\nI5RarWiQwP7GlhaKJkfRqLB9GH66XXjGT7x94Q/qYmD683BhTYhUnPCFRk+R8NTPxQXsfStACYDO\np8QEbFOOaK9HcyVgF7gl27Tp4EDcfeDRzv5ZVYSiiNY/+xEeO4TuYoXuKIqktxhy3ZL1eoKPzvNr\nIv1BHg2crEqcBavAq/Vq2LskGuas5Drs3mIFnxb6iySb70vwfrcWnlulsm8F3Hw7vO1D8PQaoWqi\ng/KhWtF8Z/hkYPnWzsTnuge4K+pfKiw0YD8NfDT480eBJxNttGnHDrwf/Sh33XUXO3fuDL/+o6Eh\nmkZGwnQIQNX4OM0DAzh8Pn73jW+wvaODx6MC6+6ODqrNZtKjssYdp07xjTjqwa3T4XG0ssEEp6qh\neFoyixDmMsnJn56mYnKSvokJ7B4PKwcHqQuqKrb09nJVWxsb+vp4+N//HU96+gzpVaHdzvfuu4//\nq9dzZ28vPzAYuPXIEeoSLKTQUySrihQ6HBy1WLD5fNh1OmrMZgqmplhhNPJqlLzvxYkJyi0WyqxW\n9OXlbO3unrGizqDTyVVtbeH6AIi22pGWxnVnz9IwOspqvR5bTg52rTasm24YHeXVL34RT2CcGjsM\n5MP9l8FXboYGq3CX7tmtLZYMtgyo/8eFc6bzgStNrD+XCqO50PDFxcnglhIdpbB5FPbWx3YYHqwD\ncw4oqOGArQJjOXDZCLy6AtrKFXyKhKKuYqltRDeWfOd6+PTbUh/fmAu5HpiKCuweLfQXRZ7IvkKV\ngcLIPdZfKN9LtV2O61fgQG3E6c+UDWfLE+et50qFxhlKUDi0ZMF0ulAj8egvVHGkAwqsG1d4pXHm\nNkdroMECxytBG5DP0VomM4YQ5WTOlkadoXzRnY/mwP3bVB5LoGzZyRIGbEVRHgUOAmsVRTEoivJx\n4LvAzYqidAI3Bn+fgU8+/TQPJ9ASP9Dfz1/v2sXGqGBbOTnJ7S++yIdfeIGJggK29PbyQpRMblJV\nyYvKpi/r6uIDe/bwbNz+7VlZeL1D2HXye38hPL12/lrOAqcTW2Ym2W43Xp0u5m/Zbjdn//ZvmczP\nD68MEo31ej1rDQaae3r4rl6P2Wzm1iNHWBmnkz1eBWs+D2OZUzSMjvKpY8e4paWF1UNDrAwG2009\nPUzm5YXb8f8Y5P6bhofZ3tHBxr4+jsatf+jyelEgPLgB4WvXrNdT7HCwrbubNL+f8YICLg9e53UG\nA3s2b2Y0a4qSaegtgRo7/HojnC2FCmfy6jrIw7WUAepUJbjSz0/xs70U/me7/Pv8W6D2S3DN38HI\nEvlMfP4tcs8dvAgmRyABI5ouaCuThpE6KxwKfke2DKEAOosl2x3Libye7ocsD7y8EtrKgkEMsGVJ\nA8pLTfK7CjyyObGSA+Q7PFkZKeZFw6EDfX4k4A4USoIVas4ZzJfButohhcfTFVA6Bebgd9QXVJok\nSiL2NMDKZL1uimS+Iwmkffr8CDXkTFP56k3ChUfjlUYonwJVA7ua5J9fCyuskQJpa1mkUQfAlAuF\n0/AvN8+kRlSEDuqZg3fXXFQif62qarWqqjpVVetUVX1AVdUJVVXfpKrqGlVVb1FVNaFRRa3JhC0Q\n4F6DIaxm8AUCGFwuVhiNMbpRBdjQ38/9//VflFit5ExP0x8suA27XAyXlPCm48fD22tVldqxMVDV\ncBdiIBBgMi+PSUYjAbtIuK5j1bHn9lotCadLITSMjlLgdLK1q4u8uMLf5r4+Xt28mcvPnUv6/mK7\nnRe+/GXuuv9+HrvrLoqczpjs3qeBv3+HZB3nSuGvjhxBNRg4Mz7ON3/1KzYEB4I3Hz3KqsFBftDd\nDcDB3l7qTCYyfT7SAwHKrFbORmXSwy4XqkYzw4NitcGAEgiEP0vT6CiXdXbSMDrKmmAhVEH0vP1F\nkjmA0CErLDCRA2VO0agmwx/XwD+8Pfa1P62K5Ubng5PB7ruldnYbKIAbPwqPbYQnNii0lkKmF64e\nksF9sfjTKlElbB6F1+ovTuHqF9vgc2+N/N5WruDRyHcYCkAH6mCtWRQbfg2YcuRcjbkSGEdzJcPu\nLJbXQsh3wX9fLT8frZFstbs4cVL0qbfBTbfDez4IRa7YDUzZkftpMlMy6LXj0FkirxnyZRBJ80kb\n+yuNUBdV2vKmCbfenmCweLkpokhJhETdjj6NfOYQXXK8RgL7378D7rk2srNXGoUaikeuRwZGkP/j\nP+/ZCsm6o73A/3eTJG3v+wB8KV48nQDntdOxcnKSf/n1r/lSTw8Z+/ax4tAhag8dosRqTdiVNZ6f\nz9F161hnMLBGr8eWnU0gEODrp0+z4/RpbopTjlzZ0cFtr7zCN06dAmDQ40Hn89GbZ2ciKkjUW+H3\nzbHH+uKt8OWbk3+j9UYjV3R0cMPJk2xIUNzccfp0ysVfm/V6eqqrue7sWdJ9PjbFyfP++yrQqrB9\nRG7Qdx44wMPf+Q7D7343dWZzeM3EyslJdrS08PPTp+UaBQIxjS06rxdz1Go9L01OUmMyzdBSl9ps\nPH733awOKneKHA7WGgxsP3duxnfRVRK52TvK4GRwsMvzKBhSZNj76mfKrO68UQLYQnC0VmHbcCQj\nXArYdfDWv4Fms2RhrzSq7G6SqbNHiaXPFgKPVuiB4ilp5T5WdXEaMPY1wLGqCPfbUaJiyZTB84VV\nEgg//TbIDLYMuLVgypZzNeZAkUvuS3O2BNOhqOB2vAqOVEt2/tBWhTXjUOCeOftypkugdWuhygam\nzNhrMZYjHh8erWTLNXbheztLhBP3aYS+cKdJdv1KE0zHZdNVDmWGUkQF9iXhr0PITdDtaMiXgqYv\niio5Wymc+XeuV8PZ/PEqOFcyc58eJaJoiW7UCUOBteMKLwSfB1ca3PFmSShdWinyTsxiuHheA/bW\nri4+9+ST/NOjj5Jtt6N3uzFPT/P4XXfRHNWp+NWb5CZZPTjIumBw3NLbS7bbzV6rlecGB9na1TUj\nQBY7HDSOjNBqsxEIBDih11M+OclgvhQWQhjJlYAdunyTmTJlealJTToFrjWb+fojj3BlRwfZC1y+\n7LrWVna2tLCzpYWyKJ55KA/+4w1gygKvAu1lCtt6etjS04OxqIiKOP+IbV1dGPPyGPN4sOTmsiHK\nB6Q0uPRWCIdsNjb39lITR5NUTkzw3r17Y/w9bjh1ig+9/HIMdQLQW6QmdGbTqGpMM8F/XRPJKECK\nUdZMwrMbkIcgUQY0F5yqUNH54cQsPhdzhQrc/h55KHc3zPz7mQqZeS2mWHikRoLByWpRRVgyL3zh\nVAUOV0OBSygJFegqke+irUxohFs/DKsm4GCwgDidFpkJGXNFNYIG1puEr42OFC4dbDXCvVfD480q\n3UVQa4u0r4dwoF4y5qkMOFED7XGBNaAVms2QL8G/dDryPOgLJICjSAH0bJnQS13xgVJVZ/igtJfJ\nQJSIvw4hPTAzYPcXSkYdj9F82DoqRcPDtUJ12BPUVayZ0FomUeZsGWEaKRoujcqzwcLvc6uFtmmp\nkv1tMSqzdm+e14CdHggwkZfHW44cYeC22+i4/XY6P/IRdH5/OIDpC+C7b4BXG6BmfJySYAFs5fAw\nV7e1cW9/v3gDJ3Hoe8eBA2R6PDxtNnOqu5siu42yqdhP1l4mI+PJIBe6qwk2mWDbKNy3PfG5K8F/\nc7G3nC++vQO2jIK+SHi8ruLISLxmaIjGuOLkjpYWrmpv5yOtreRMT7MpKuNfOzCAPSsr7L533GCg\neWCA+jglTI3ZjCUnJ+b1UquV3ASfr78gMY3hU2Agqkh033b45Tb5eSpdHthqWyTLdmthLHdm48Nc\nMJ0mnN7JSslEhlJ4P8wVv2+WB+lALQmrz84M2DgWKy2bL3Y3SKccABoJWEcvsPdzV4kErPVmoT2G\n88R0yZYlXOsmI2R7YVdD5D12XSS7M+YIhw2gCUggjUdnkfD/1Q4wFEKeZ2YL+SuNMmikQrlTYkBv\nkRzTngGdJWqYzwahsPqLhDcej5PjOXTQEgzYAUWO+YVbYeVkairKp8CDW4QCCxVQ+wsh35P4fccr\n4ek1Kr8IygoTYaBA6E0VuRaJmnraS+U7caXBg1tBF9UU7dKqPLI55Wmff/OndQYDO0+dQlFVtD4f\nAUVhTVR2/b+bZRoUX1gqmJpi9eAgf5yY4F0HDoQLY9+4ER7aEtluvV7PTSdOcM++ffSazeQ5HZTG\nX1BFVpoIve/ZNQrpPhnZf3Z5cl/ebZ2dXDeP5bXmAkM+/HZDpCBkzEm+vl0ojDcajfzVkSPsmphg\ne2dnjPqj3GqlzGLhQFC3rrfZ0Pr9M+KRBlBUlcooU6vrzpzh6qD2OnQsr0Ye8EReC6400Beo4Z97\ni+DJdfLeo9XSfFFjj0yNh/Llge+co8NbtKD/bNBdzZMOayfmFvTe/wH4tx1KQi7VmiHTzyyvcJ/J\noPXDE+sXzjvvagJ7VGaV456bWf+/7VB4cMvs20Wjuxhu+cjM1w/WwUqLglsj1EhHKdRHcb/HqoLF\n0Kj73pIp9AQIhxvSPR2og2MJZjiDhcL55wQDsleB1vLY67a7ASZnma3keRQGCiM0nDFHBuqBAhlU\nQL6vxkmxZI3HUJ44CX7vOuGCP/NWkfsdnYWKOhTUcd95A2z/RJCWKQQCid9nzZYs+6GtYE3AX4MM\niDkeURt5tLG8f/R+mibhmTVSH4imc05WJi/ehnDB3PoKpqZYNTLCqpER8oJZnQo8tBmuNsDx6pnv\nyZ2exq/VcnVbGxVBA/4n18KjmyLbKEC12UxfIIBxeppMl5P8BAxGXxH8ZoOMpi82qegLoLtEKtd/\naJ65PUCu2z2DLlgsvr0Dto1EMoXhPMls4j0VTlXCxs9Efl9jMJDm99M0PBy+fiBUx1qDgQNWK+ec\nTqy5uVzW1RWzrxC9EaKU7DrJRnR+P9keDycrYdNnglrZApmm+hIENWtGJNM9VyI3nlsr0+wD9VLI\nyfEq4YCtL5ApdV9RYn/heOrh7hsUPv9WeehPVEGlQ37O8M4e9JzpwpU/sV7lXbfF7lsFvnyLZLtn\nZqFXOsrg5SZ1QfJFt1aK2+eiMk1nOrw2Bw7+1xvVcCFvrvjmDfDSypm8594VCgFVstRDNTLDzI9q\n7nXpROEQDWumZLdeDYzkRwa9gDZWiheN/bVwoEF+duigI6rBxaGTmdWsdJgqXHNPkYozXQYLu07o\nqWixbK0tMVU1mieF1OdXK2R45b7c2wiOWaSg3jQ4EAyYWV747vUKPSUK3hTf+7EqmZ0k4q9DqLfB\n4xvk2UimIS6egn+8FTYblRhqxZcGW2Yqf2NwUe1VT1VKMDlXIhcufmzb2tnJu/btC/PatgwZfQ/U\nxUp53r9nD1OZmQxkZaH1OtAlcKQMTal+dKUY0IQKEkpAmkLe9wGFP6yDl5tk9D0fpSJDPjzRDKei\nuTyNSK3is+zfboS28ogBzTqDgX/67W+pifLpBgnYzXo9x0ZH+WZ/P9edORNDe/xyK2z7ZOy+330b\nPLYh8vu+FfJwHamRrLkyAY8HUiQKBePWctluzQT8fr3sw5kmWXyoMGnIh5JphQrHTM8IjxZq/g/h\nbVXgkY0qD2wRnvxoDWHtr103u1LkYLBjr71EjHsavijV/Xuvgq2fglcaZFo7G8w5wu3GdwTOBUdq\nJBOMfggHCoWDT3U/jeWIxGw4N7EzXSKcK5Hu07XmmVnZoVqVsRyZ4aiKDGSzLg2igaJpCf6jOXMc\nsKKix0hubCA7UAfrzOCeZW0Onwb6ihRZiSZL9rnCCi83RgqmAHsa4USCpA5FnpM9DSptFcx/uSRF\npHw/vErlUK2KI0n2DJJBn6lIPRjkeOTZKnQlPxFj8LtxaWfeFfpZjCwvasB+aKs8HKPBrC2e81kz\nPMwfvvENVgcpgMM1chM0TUaMaQC2dXdz87Fj9FZVkeaaJEG8BqBoCv71xqA+M3g9j9dIFXgsW+X7\n18PXb5KW0njt5WwwZ8s5pdJ7P7BNRtCJOB6ufCoiZQrhybUipwt1aTbr9Xz6qadinP5AvsACh4Nz\nY2M8MzrKJ595JqxIMWXDV94kQTZUXPVpZEDaHdUQcKhOYYVFvo/eIshNwuNZsiQDs+uEstAGYDwT\nftccUQ34FNAXyvv1BVKorLHPDEQDBRJYfx2cLbWXiTzs6kH41k6ZHk4GH4y+Qsm4U13bVxpF5+pN\nk591PugthCeb5Ty7i+SBmwt0PlHxzAVtZZFBZ1eTfJfRMOZJgSuVYmFPA2wwCef8UApapKM0MoW+\n6wbYbIRquxJTI5jIkueoqxhQZBB7fhUpA1EIRS65j8dy5r8c2GievCf0ne1qEvnfbJhKl4aZoXwY\nDl7HsimFnpK5nfNSYLhArmVf0cIlqCF4NbIfv5J8iG4vgx19EdlqNHpSZO9wEQO2XxGKorcQ4Zgn\nZ3aarTEY2L1lS9hdb3+9yIeKp2MDqgbplPSmp6NxjSVd3qetXCRC8dVbW5Zwfa/VSpa0epx5TU8d\nOtGafui9sOoOaedOhOdWgyXBtC7dHzuN7iwRTrHeAruaJEopQH9FBQ0JLGh1Xi+j6ekEfD5Kbbaw\nF/gX3izF1S3GSENLS4VkXdENHceqVMod8Ph6CQqBZPmgIhSSoUAyDVea8IeGfFFGmHLlNUOwGaK/\nSMGnSAEsXkHQWyQZ3cPBAPX7ZqEsTlTKYNVWFsnKJ3KkePWnVckz1VcaI8ECxOhnd5MUs09WM687\n/WiQ1mibZTr/qy1w3d/CTR+VY+9uTMxvrpwU+uLf3yC8ZTx2NYnWeDBXBrBEA5MzXRYZuOUjwrm+\n3AhHqyQwnImasb1WK0lNIJidKgEIaOa28Gy+WwKWKVtms/OCIjWH0H28q3F2iRqIt8jxKtF9h2oL\nmiCPfCHVNXvr4Y19qRc2mAtCz7c9xWCjauDVxsS042w4rwE71fTuaI0E3/4gFZDlnRmwdX4/N0SZ\nuO9fIcHWGNSSRuOd+/eT5XLh84wmbDkFme5eNpzaMAaEhzxeNbfOo4AigbrYJYEryytZ7VhcFj2Z\nKQEgUVHBo4GOsshT+od1ohM25MOrKyIh6rq2NhqNRk5VwifervCJdyj891UK1WYzjuxsbjpxgoyg\nBHFPgwxwr1VLUXd/MFAcqIcrhyQLsGXIeY3mymeusUnXmifFdDjksNZeKgZBAS1sHlNosgS9JjIi\nN72+QMWVJllHa0VsFOotEmmYLUOyxt83S4HKEizu1NhjudM6q3QPbvwM/PCq2OAc4kvnSifMBl8a\nbBhLnWV/9U0Kd++EEqc0c7z7NhlsEvGbFh0Y8qQ78IPvm3l996yQAlVnKej8ibtF77xR7AHGsiUI\n11tlau5Ij10bcV+9DJ4hmIPLcs0lEGX7Ihn2+AKCZcm0QkcpPLtagvVsAx7IvTeli+2C9GhkVhT/\nDJ1PBLTCfcdz+/NFyMwqVUfwYnBeA/bDKaZ3f1od1FkGMZ0Gx4KFpRNV0qkVDb8ipH93kUwpRnJj\npV7Xnz3LY3ffjd92OmxUnghHa0V5kArudJHd/eRK+f3x9XDXDUrCzP2bN8iXsz8oFWsrl4ATvybc\nribYaEp8bFsGdEZJ+37fLAWW/iKZEcRPp++/DM6WqZwrUvnWDpU1BgM6r5d/fPzxcLv/r7YqNExK\n0JvIhP3BILBvhWS968ySjR2rlsxW1YgTmykn8SwghByvQlexXPvQzdlVpNIbVI+YsyPBYShPPoc1\nQxo3otFdLAX51eOiSR8oiEz3D9WKWiMaB1YINZLuF8688Yvwj7cqqEQ69lxLOIVuLRMuMlGmOZgv\nLpCWDOgphd0rpKbSaEnMb56thD1NklXV2YVCCmE0VwJTZwmgyKAZT4ucrAy2f5fK93SsNsLnDuVD\nR9Qg8dLKWGVGWymsMTOnJz3dr9AftFt1LuBaqqrK0WpRaoToqdng0kkSkBdFw1myoMoemSX8OcGe\nCVuHY73FlxLnNWD/76bkU9g/rYKJqBtrKA9ayiX7+Jv3iKFMNM6Wi/5xMkdu2o0mhRdXRv6u8/tp\nHhjgULUnLE9aDM6VyIPzxVvh/9wCz6xWueUjsRzX6QrRohryYqc3dt3MwSokJUyE4bxINj+SKzra\n0+WEO6PimzwO1skx9jZI9po1beHoJz9JjstFwdQUKvDiykiTS2eJZDvTaVKQMuQLv3igXiiggqCC\n4Ey5tGinmj6rqLy4UjI8f/CBGioQTTlI4ciuk2MN5UkwGsoTTjX6XugukSDXXyAF1s1jkQd0Whdr\nhxmGIk0Ge1eAxi8m9t/eofBK0+x63/nCmAcbxxTuu3zm3366XTT8lpBZkkYKyeY5mFRp/PCjqMw9\nxF+HMruhPGYY53/uLbDONFODDJKZu4NNL+NZcp1jViPXyDWbCwKqKs+Zk/kX7xA67KfbZeA6lahA\nmARVdjl2CG1lkPZnvEbzqWoWdP3mgvMasJNN7yayZPoaXSwx5Es28883Q6FbpnLRHNaBeqi3Rq6C\nH5VHtsQGgRrTCPbMuXFns2GoQLLQUHA8WSnfweWfkBmAXxEVwvqxiBlNCKcqpNobmh6rSFdltFl7\nNMazxcthJFec8TYbIwNAQFXZFWWk7tDJfkMZ2QorTAVMbO7rCy8AcbZcrr0+mAG7dMKj/qFZgqS+\nUD7TvnqRnE0FA6UlW1YemUyRHfg0wtVWOpPckRpRj3SUyuBryRIOWqPGTnH7C4Wn7y2R2Yx9nkWu\nyRxxQLvvcpVfbl2a7zwehjyV711PTDu+RysznP64Ka9LByNzWFLqWLXMJkLdebuaYmcT3cWiIggl\nBpOZkhgcSqaSUaQI31om2fVG08K4URCu+2y5FB8XguE8kYSemWdna6FLgn0YSoQqXUYszmvArrFJ\nN088Xm6CTWNxUyaNSMR+cRno84TDjQ72exsUvJpIeD5cIw9StPfDaG6wtXSJPtWhGilAWbIlA3ql\nUTr5bvmw8NY+TWKP6IBWHpxQlt1WJpxcUqWAIhnrdX8rGVJ0K/ZgcEHQ0Cc/Wi3XKUStFE8rDGZP\n015fHzZxen7VTB1o2RT857WyYgiKBIZj1aLuiDZ0ilewxGMqTabLmiQNBiAFpEN1QV4yeA4rokx6\nVCSzDilXTpeLWme+MOVKY0qRa+n462j0F8tg8pkoE6XfNct31TtLNT8ZAlqhoO68QeSkj6+Pvf6q\nRu79UIDeu0Iy8FRBuNAlSpFn1ygzqKT5wKeR7yg3QR/DXGAolEF0tnsoHgdrl97g6/WK8xqwO4uF\nj91fLzxjiA9MdmPluxW2D4vMJtMbKZT5FTEjj9Yo+tJkmzveHBHUD+dJ88ZSIaBlxtTmtXrh57pL\nglxvkis4nCuU0IE64eNXxgXQeFQ4FRotCodqYnW8/YUS4ELtt/vrIy27ILrnzjKR/YW6GJ9bM1MJ\nM5UGp6pkSg4yCFU4JLNPtS5ePEKZbLLCLggfeahWuMkQCt1KOKhOZsmlsAb3tZhCT2eZUEiz6X0X\nin31EsR+coV8lz+4Rop+i8GZcuH/u4vEwrQvLpvM8oquHcTwKMuben9+ReV0pcziUskHZ4NbK4Ox\nzr/w+fxCvstEz9l5w1TR/L2WLyEscPI0NwwXwM29Cne8WZbpcurgyd/IjZWIz32lMZK1WTIihbLd\njRKI4z0pzlTCDX3SxXbfMxKwE3U5LjV65pDNdZTCDf0Kn3+LZMe+We6Rl5uSS+lWT8CPrlL4xVNq\nWCkTglsbUpjI+53pUpyN31tv8EGOpg7q7AplU+q83PBC7bbGFFmURpV91tsi5+VH5XCtwqeOqfQG\nzYKsC/AYudDwpkmn5S+3STEu1xP0IlkEzDnyLxmsGZFVXXY3wGzjg10nUsgsrxSqF4qQ9lo9L21j\nlwD8Wvj5Ubjpq7Dx8Yt9NgvCeQ3YIME5hGv0sONjUuQamCUT6ApytG6t0ColM9eiBaR77Uw5/OMh\nCdjpl0qxQoHdjUtz458ph5OVKv/5olAYaVFP8GQmODMix9nTILRHvP/3WJ6I9aNpJlOmGrbXnCum\ndbKfVMuF+RUxoa+zRs5Lny8ugCoi6StewpnQ+UbbLDLQpUZXsWSqo7kyw5qa5SkdyhOTrRv7Fhew\nQzPgRSTYs8Ong+OfAH86pLlg+31iOJMMXbfCyhekCLJYnP4ITK4E45bUAVt/LZS1QVZCm/+Ligva\nOHOoXirQZVHcZjI4M8TWcX89/HF1ck2nLUv48G/eIDfupRKvlxLmHFFR/PPNUqCJzs6G8kVhErqd\nn1sj6+AlwquNsXWDs5UiEZsvXm1MLblyBf8WLYPsL5KvvD3YEJO2SFrh9QxHpvDkP7xK+Gv/LPK2\nsVwomAbbQmkhnw5O3R7Wtqfy01g09NfDwX+GrrfBnrvBnGLFiIACv3kSzEnMfuYDfxq8+g1Y8SqM\nzWKJ9/y90PGuxR/zPOCCdzp2lc49SFQ44atvkiJNvBIjGkeqxStid2Nik6HXAyYy4JeXSfNENOyZ\n4l8wnCdB+5k1IjO8mAh1eU3FVf5XTYics6tEmZUi+ktHlUP6ADJn4a+BcKdwvC/0nKEg1WrWAAAe\nO0lEQVS/Hp6/lymdNFnNltEvCkNXQXE39N0IJZ0wnsK0xVkB/gwwzhJg54KW2yHbDLYaMKUYAFRk\nEBndlnybi4hLOrxNa6UjcrbKtzNDsuzQckWvR5ytEAlhIgaj1iYyv1OVkrnO5kdwvhHqkpuMk9o5\n06VhqrdIXVBjxl8SprXinjfXbr8T1QuX82G4DlxF4Mug1HmeFz0evBq8wQOkuVMHbEuw8jqaQGo2\nH0w0wZ67wJch+7TVgDdJd5i9Cjz5QptcgjjvHPZi0Fco9MlcMofD1VDqPD963EsCCgzmzfTkAChw\nK3SWqBgKpGmhbxE85lLAlCM+IfGFyfbSSOFON0/u/C8N/QWiskll5blkGHij/O+swKfVM1QAyr6v\noZa2QvNTS3us4ctBCWZg/jSU8fXJS5zWekh3LC5gd90KT/4Kytqhf6e8VtAL5nVQ1TJze/M6KOwD\n4wbJti+xmeAlnWGP5ktRLZkfbzSmMkQ9sZiiy6UOW1Zi2ZQflY5SWUxg7BIYsFSNTKvjvzd7prjH\nGXMXb7LzesdIgdjVzsZfzwv+BPlZQIGh7ZCvB0clxuD3ovbdCPv+NbLd6Gb4+aHFSeJsVeDLBFuw\n8u3OQzWnyLCtK6DiDIxtmPk3w9Xw8AupjzeyFf7wEOQYI8EaUHKNYEqwTwBzM0pRv/zsWKK16ZYQ\nl3TAhvlN85bSS+LPCa40McMyZS9sOa6EmCqW1rcFIpkuOt8tDVULnr7/BWHJ7+eftMLoptjXTBsg\nawIKDeCIksPYqiRQDgWtJ1/5NoxcDgM7Fn784SugtJNw2uqohImVybe3NIHWA+580U9HY9d/QM8t\n4Ehxw5+9LRjwYzlwVfHD2KbE7zFtQA0oUNy7NNz5EuOSD9jLmB3mbFFfRHtSLBq/+zUcjVryJqAB\nSwot3xzRWyjFx2VcYDhLYWINtH0g9nXDtVCoR9G6YzNKRyXUvgZH7oDhbUJl1O9HafnYws9h8GrQ\nRuk5nZXgyQFXMK135YMtSo9qWSEZeXFPbIAduB4mG+X8+lMMIB3vih2EQvBmJg/Y5mbw5ILOkTpg\nTzSCJ8o7w5sB4ykGnyXCcsB+HWAwHxQVbEuZkU2shCOfi+gFj34GHnp50bvVF8nqIZcMHGVw7q0i\nbXs9Y2QbZE5Ae6xcTRnYAQENqqqAI+gS5c0Eb7YErHNvgxfuFUWHqRm14+2RomEIjnIwpZDnhTB0\ntQTDyNGhcAAmgub2+7+C8sK9kT9b68BVAFmTscHzlW9DvgG0Luh7U+JjmdaCOy+xIsRZAaZ1id9n\nXiODlS8dZfSy5J/l0T/Cz49IkLbUwy8OwiPPx25juArGlkCSGIXlienrAJ50eEN/CoOg+SKggK0W\n8gdFflV3APZ/BZxlklXokiwbvdRQETnWlofOT/Fn8Ep47AnItMBTv4TtP4Mb7ly6Y7W/Exr2QJZ1\n1k3PO0Yuh6pTQnNMNMmUH1ANV0uvfd4QiqNaxmdbDeQawboCpWGP8MzTxeDPhJrD0Pk22PCE7FcF\nHn8M0jzwkVuSHz+gSKaujdUpKjlm1PE1UH0Cut+M6omqVFvrJBPJGUMZvUzOrW9HROlR0h0ZZOLR\n8W4o6wBHAttAa72chycLdFEZvzsXposkq8+wo7qTdPdZayVzLz8jgVpRobwVLI0yeOUGl+j7w8Ny\n3Uo65T5AhaqTkWu3ACxn2K8T7GtYQl7YXi1ZTd4QHP4CHP+kZEIlXTC2cfb3R+PUR8C6AGcnkGnv\nkw/CZNPC3p8Kx/8efv1HyBuW6XH6NJz82NLxltMF8MRvUV78wdLsb5FQRraLrK28FdrfIy/aK0TO\nN9kEfh2qPRjc7DWQPQ6AalorHLc/mFVrvBBNi7TcLvfL0PbUBcmJVZBhg6nYDjgVv+ieHWUw2SD7\ncucKPRJIA1chuApRjZukaPrcT+Q7U9MlG3aWy+eIR/t7YTpJwFXToLBfFCHRMK+Fon5AI+cysQp8\nCYoxPbeglLfCwE7IMUHOqCQ2pR1guEa2sVVLsHbnCU9puEbop2d/IgPXArEcsJcxE5YGyB2VrEx/\nHez9umQeOabYgHbgn2af8h34MnTfurDzMFwb+/9SwKeDp38OB/4FdHZp5ABRJJSekwC0FGh7H1S2\noHbdKpzrRYY6skWyQldeJGCfvl2CDBrw5kQKeLYaFF1wCRhnFZiiBunRLTBwHRz+rNABL30fND4J\n6smUF+OrYO83UIoGZv7Nr0MZb5YCYsVZaaoZ3SJZcP4QoEhGbWqGA1+BDDsMBoMiWihvi1GAyPlX\nyyzCmISnBpTcsZnna16HkhNc5NqfJTPM8QRUT9fbUEMFedMGGAtqttNcoH+D/Ny/U84toJN7bGCn\n/Cs5B0/fL/Ifd44E8MErk55nPJYD9jJmwtKAkmkDb65Mo0s7pRijEukAU4ED/wwn/y75fgKKZCnG\nBWYU+jdC/oD8vxTw6eChl+SzOMpFhRANywo489eLUseE0fJRQIUCvTygF5Mjd+UJLzvZKAOuqRme\nfACOfSoSpF0Fkq0C2KtRNUmE8t484Y/bPgD/rxXKz4oUrsCQcGBVXrxHaAN7Fap51cz9uQpRx1ej\ndL8VCEhmP3KZfBfZweq0p0C6FA/8k9AR0ZyV4kXpvyl2n8c+BZVnJAtPApUAvPZF6Hh7RDtpWi+v\nh3adNyID73M/gscek/vZrxVaZjzBKt2uQmlCApS+m0FN4L9guF68U17+Htx/RIq5v3kSLHNzYFsO\n2MuYCUuDTFVBbs7BK+Rnd1QHmGm9ZGUd74oUJgevhN89EtmPrU6m0qML7BozXCNTV/01if+eagoe\nUOCVb8HPjkomqAJP/xLQyP48CTxlJ1dJkIjP2OYLS51cn5Gtkl1lj8OxTy9un8mQrOuk7T0oT/1C\nfh7dKnwvWghkyCA8vgamSsASVDZMl0gGrgK2+tSDlmmTNNukucIqDTWgkQJmNJwlqMf/Trql+m6S\nbD0e9hqYWInae2OQmklDGblCZjxpUfxyUT9UHQd7XKHGUYXaF3XcjrfDib8TuiQV9NfK/vd8C37S\nDsaNYN4gtFEQKgE4/g8ywI2vEWpw6Erh96cS0DDmNbIfbwZq/xsS8+coct1Pfhyyx2R/pe3w62eF\nCpoFywF7GTOgTK4W/hCE7wsEb2JbHYytl4e67waUmqPg14UbG5SD/wwd74wE0vE1MgUc25A8sETD\nkx1RILjyJSMcvkIomum45VxO3Q6/PJh4v9MF8Oiz0PVWoT1+eVC48NEtMHwZKW/7LPPipGsAZ/4G\nKk8Hr5sC3izhx1PBmzn/LpmRLfDj9pkDlwrs/Trq6Q/JNqPbhLIIoX+HZMPuqGvqzRWzdHceiq1W\nvtfZ4C6Q+wMkKx+MW7X45N/L4DCdwo/YVSSUis4uwXiqFHVkq3zn0Z+r/43Qf+PM94+vhkC6zJyO\nfBqe/oUUkZMVI0MIZEi2O7pVGmsefEWoq6mo1tKBHbKfvptENbP7W3Dq45A3knifvhwo6oNz75QZ\nSzKNuaVRsvGBncjyOjdAjhl+9+iss7vlgL2MGVAtDaKPjcdUmTQy2Gqh702o/jQpRHa8G2xVqL03\ngc4pNyRIwM4fAq1b3pPwYMDQ5ShP3w/3jKI8+aC8PniVVPl92fL/4NWR9zjKhDudbJg5DTdugJ8d\nk4AzukkehmyjZEnOEtlfKpiaUc+9TRQEc4GjXAaX6M/Tcjs4o1YlGN0sdMPY+hlvD+N3v4HfPDM/\nOmb3v8H4upk869CVUvCqOwS7/w1l+EqxMw0jycwk2wSOSik+eue5bMxkk9Q5QhRLQANHP526sSWE\nAgMU6iP7mVglnytm0Eg2m9KI/4c3S+xTi7rBnOI6J4LhehnQirsks485ZvC4E6uh4jSc+Af5nMmQ\nY4J9X4PydlKH1+i/KVIXsFcJVTLHdy1jGQJLnUyRE6GoX7IS/XXycE0VSxHr+KdEslTcHSlMmpvl\nwS3qT6y+OHU7/PQkPPY71IlGyBpH7dsphUz99aCzyXYZtjA3CMALP5QCVVk7yuEvRF5vezc8uBty\nR6D3pgiHadokmXqiKXk8piqkO+6FH84+K+i+GX7ShvLC/428NnSlZGMxjRla8bJIVtC01Et25yiH\nF/9r9nOEmGaW+EFLOXKHZHqGq2H4ctSuv4KpOay6kWURjbK9KrnCIik0UHYuci6db4VM69yCp84q\nxwSh0Ar7oW8neOboX+DPlPtj8BoYSkKfzYbxtaIT92cm30Z/LazYk3rg9WYKbZiIv06FgE5mlG3v\nTbnZ6zNgD20X05elKB79pSGgEV7RniS4pTulMKdzCEc3tlEq+kc+K7rZNHeEszavleCVPjXT/cxa\nCy/8QIyArHUy3bU2QMVZlD13S6Ex9MC68yKFx463y2ChvxpGLkPtuVlkXX074Y8/leKU4Q2LuwYj\nW2UKfviOpJsoh74kNEvJOdT2d4cDnATLXmY8WtY6OPOhxLz70c9CZYsMgOfeIfzmbNj9b6LvJYCi\nj+JwHWWonW+RQdWfJdu4C0Q1MRt0TpHVOSojBcj5QBtUSdiqRLcfGnBng35HrOd1rlG++7kMMhcS\n/iyhMQIpzI0sDfK/fQFSVtfsKw+/PiPa3m/AU7+Ae/vg5N8m3qb7luTdTn/JsAU1uMluSp8O2t4f\nMchR01AqzojD2cTqYIYRVIVMNslD59OhxPsLd/8VSsVZGL2cmNtw8ErU/h1CiUwEVQUTq4R7Pvgl\nUVxkWIQvdBdIVr/rO/DEb4R+WQqze0++UEL7vgqtCTKelo+gvnYHoMLgtTJVPvXx2GAZj4k1Msjp\n4wYTbwac+qhkV64iSJuS48Zn9/YK2P9llGd+JgqPkW1CEzkqUfVRdNHJv0epOiX7Atmm6njqIBOC\nxiP1Bp1DgtN8MV0k+vb/1wrpLhi6Yv77AClSKr6FDRoXG45qqNsvK9ssBCE6MQlenwHb1CxZnc4J\nu/5NOs6i4ddKQH/5+xfn/C5lhDTYyTBVBoF0VG+EX1RN6yIPl6NCeGRfugR/Wy04y1CNcQ03XW9D\nTVRk8+aKVCx/MBJ0XEVCc5z4O+HDo818rLUSLEvbl9Z03l4rzUPP3yut0KHMWH8tvPBf0kASUgFM\nF8ORz8CJT0JlVLCMR+4ovPLvoqYJBeS29wsFEHpQTRtkVhLV1KE8+z/wk3aUnlulkWWiSegGf6YU\ntpzlws/7tXD0U6jRjST+TJnqzwUBjWjvc8bmfJliMLZRltbyp0sjyVwGiUSYLgo2x/yZNmIbrud8\n+bL+mV6RFPBmSKDwpwmHWdoGz/xcHoqQ/23n24Wv018rfG2h4eKcqysfnrkP3nwH5Jpi/zbRKM0d\nb/vUhfXktTSgZNiS07eTDUKLRHcfOqNMg6wrpDBp3CwPnaVJBgFNQL6bdLcElv4dEvQSYeCNMwcN\nXwZM1c4sGk6sgcKeYMV9iWFulkJc161w5oOSAFjroKgHRqKyx1Cg2vs1uc+SYfAqMSx64jfSDq5z\nyIBW1BO1kSINPO3vgbL/AONG1PZ3it9H3w0JdqoNFmWvkXXbsicW7h+tpgkvXty38PfPdXBIhbFN\nMmNbxgwsKsNWFKVfUZTTiqKcVBTlyIJ24kuHR56bXTcZOubL34WWDyffwLxOmhVCBSfzeijqgkef\nAXswsBz+AmRYhTc89ll5zXA13H8ocZvrUuHMbfDrp6VQ59fC409A782SmcXj1btF9xkvlTpfCEVo\nS2NM88AMBDJEv5qsgKemiU9Fx7shbzTynoKBCF0xdJUE86kkU141babe1rYiucLDssDp51wwVSac\nvMYnqgWdIzZYA6CIlKysLTUl48sWrt6yQgK2XweZkzAc1+k2XRTpRjxyhxQsPQUz9xdC2pRQLUfu\ngLQkq1XPBb4McFaipLkWvo8lgTKzqWkZwOIpERXYqarqNlVV595fGQXl4L9IRf/Mh2bfeHIF6uHP\nwd47k1fwTRvEoDwaQ9eK/OzRp6W6bmoWfm2yQfSx5tXw29/Lx/nNU8mXD0qFgAYmV8g/V4KmDBXY\n93UJAPcdhz88IlrNHCMc+0SsBnd8FXS+GRp2oxz5wsx9LTUGrxA9r70CZXKV6FpTIZWuFqS9t/X9\n0lgRei3PGFGKdL1FCkt/LlDTRGZmbpamkkQwXDePBiGN8P3mZmnWiYdxo8xKxtZD6/uEYkoFVyGc\n/aDwz8Pb53gOCRB00lOXYIHyZZwfLAWHvfAJu3k16qEvQM3ROa1SrOz9hkwpCUiQT4SxTWJQHo++\nG8Tg58HdwpEGdDKKF/aLTWJp+/9v7+5jpCqvOI5/j8vLCihICyiysqtFK74CFrXVlrZa0bRik6bF\n1Gprqm3qexpt1aTqH01jrUWikhrfqqZqjFrFxFgQHcQaRRGQ1wIKKPIOigICC3v6x7njzi4zC8zu\n7Nyrv0+y2Z17Z2fOzs4995nnOc9zozVbswOe/WfLE8LOrrGecCmb+8ODr8B9r8f3OxftnrSXnx4D\ncitOjkWVNh4RVRTrh0Zlw6IfNd936s0x8WLVsFiLYnOrS8bv6NFy3eC2NHZv/mRRGG/hCWLmJZGU\nHp+Irz+qeA32PvAmi66KgiuceJPFYNr6I2Ntka17HhHPnI7qc/WuUVr45GPxvdisukIbhkTXSv+5\n5fcbQyR+iK4VSaWOaGG/aGZvmdklu+2ddFvp2VtO9C0PmBPdEZ8OjBYvxKIoG1q1PD6qxxeOiXUG\neq6BUi3Ptcftvl4vEBdF/EYMChVecqhxfzh0RkywYL8oCVw1LGbs5b34V7jn7ZbdJUtHwdyfRgv9\nnhnRmtzSP1pg/RZir1/T8tmnXxkDaRis+FbUBednmnX5LLppAD4cAYvPiji294mZYm9f2vJPmXoz\njFsOj7wA7xWZ/QWR5F8YB+M+iNbzhyOS13EwTJiDTbsxbu/sFvXLjbXxN3w4suVsr3JsT05WhWsf\nv//t+L89MC2qPtbt4+SGL5vG2hhc3Zt66MYDYPDU4pfS2hf5//vOSl6FV9rDvB2ff8zsEHdfZWb9\ngMnAFe4+LdnnHPDraLEOfQKGbIPCipVZF8ZKbuuPipZJ/ctw1EQ49Q54+pFYR+KKIbBfxGfPPoB/\nfFhME+26Oep9fzNs9wHD8UuiLKg9fWAD34Cd+8NvT4wkfPf86O/e0QsuPAMm3wbvnon1eR/c8Mba\nlv2QvZfFfa/8WqyF/MkhMGFutFyK9UXutyNmWh20NFre/RY2Xxj1Kwvjsa6uj8vHN1kk4e6bkhXS\nhsJlxzT3F+f/N888hG88PAZVD1gdLbALz4Annoo1DNYdE6/vslFx7b6VJ8XVQOpej08D7Wkt7r8+\nuk16rdx9PYV+c+MTRSUGCb9I8v+LZaPo1FHn2o1RJbJBJa+dJ5d85d2Cuxf9p7crYbd4ILObgM3u\nfnty22EnHJ6LxXfG/jhaixAlSBPmRcLJD9IMnB6LoI+6Ka5y3G0LnHUNDHkhKibunQ5e01wy1fBS\ntNIPficGtE69I1olt26MsqJ2fTx16DcPvvunSCxrj40ulcHTYppx//nRz1hsAaG8+hw2eCo+8i6Y\n9LdYh2NpidYwxEliv6YYpW9qtY7DwLdg5J1w4sPRsn/+7uYWasOUiOfsgkkeW/vC+HdjoCzf39ww\nJRLx4Ffjb6l/BRucw9ecGPdvXR/cXoe9ErMVv6CVo19Yda/G+E57ulaknazjE7aZ9QBq3P1TM+sJ\nTAJucfdJyX7/vCN40GsxyDLyLhh+b3QxfJosqpJX81kk7NqP4gzfZXsk7QvOjtbipkNb3r92Y3Sn\n4FHDet5FUZv61KMdM3li4PTo09v61Sg/2zogZnIdPDNZQ3kPiaj38qjPtV1xolr39Zblb/tiwKyY\n+XX5Udhz9+MfHQbLkxKvHmtjoabfHQsHJovS/PfaGNhrseqcx9VCVo6IPtLey6OvOj/AuL2NKgQR\n6USVSdgNwL+Tm12Af7n7Xwr2e4uRuz7vxZoSq4ZFadRnB8UkicLHHDwtri33/mlRqtT1M/jJ2Khb\nbepSOqnUvRqfGkf8A3v7Erw9V3b+nMcgTs91bbeM29JvbrSsOyIZDnwLht0PU/4c3UyFyb/hJazf\nAvycy6NaZfy7cbIrtaB8wupzuNdEy1tEUqICCXuPT9k6Yed13RwTL4qNfHfbBLu6Ny/A0jAlmWww\nve2kaTtjta+ea5I1eotNMChD949j1lnrLopqGDA7aswPntV8lZS8Hsnl0k98OE6MMy4tfVXoQjXb\nIvm31bUjIp2sdMLu/A7Gxl6ly5R29G65WtaGIVGvu3JE24/pXWLq8opTo+qjo2zvk45kDbF40sAZ\nMeGita394iS4+vi4nFf3vVx0Z1etkrVIhnR+C3ufOXs3Sr4r6rk3Dd7z4uWZtbevhYhkV5q6RERE\npA1p6hIREZGyKGGLiGSEEraISEYoYYuIZIQStohIRihhi4hkhBK2iEhGKGGLiGSEEraISEYoYYuI\nZIQStohIRihhi4hkhBK2iEhGKGGLiGSEEraISEYoYYuIZIQStohIRihhi4hkhBK2iEhGKGGLiGSE\nEraISEYoYYuIZIQStohIRihhi4hkhBK2iEhGKGGLiGSEEraISEYoYYuIZIQStohIRihhi4hkhBK2\niEhGKGGLiGRE2QnbzEab2UIzW2xmf+jIoEREZHdlJWwzqwHuAkYDQ4HzzezojgysOnLVDqAMuWoH\nUIZctQMoQ67aAZQhV+0AypCrdgBlyHXaM5Xbwh4JLHH3Ze7eCDwOjOm4sKolV+0AypCrdgBlyFU7\ngDLkqh1AGXLVDqAMuWoHUIZcpz1TuQn7UOCDgtsrkm0iIlIhXcr8Pd+bOx14YJmPXiXbtkFtbbWj\n2DeKuXMo5s7xZY951y7YsqX0fnPfq9zb8pfMTgFudvfRye3rgSZ3v7XgPvv+wCIigrtbse3lJuwu\nwP+A7wMrgenA+e6+oD1BiohIaWV1ibj7TjO7HPgPUAPcr2QtIlJZZbWwRUSk81VkpmMWJtWYWZ2Z\nvWxm88xsrpldmWzva2aTzWyRmU0ysz7VjrU1M6sxs5lm9lxyO9Uxm1kfM3vSzBaY2XwzOzkDMV+f\nvDfmmNmjZtY9bTGb2QNmtsbM5hRsKxlj8jctTo7NH6Qk3tuS98VsM3vazHqnJd5SMRfs+72ZNZlZ\n34JtFY25wxN2hibVNALXuPsxwCnAZUmcfwQmu/uRwJTkdtpcBcynuVon7TGPB55396OB44GFpDhm\nM6sHLgGGu/txRLffWNIX84PEcVaoaIxmNhT4GXFMjgYmmFlnL01RLN5JwDHufgKwCLgeUhMvFI8Z\nM6sDzgSWF2yreMyVeAEyManG3Ve7+6zk583AAqKW/FzgoeRuDwHnVSfC4sxsEHAOcB+QH0lObcxJ\ni+l0d38AYvzD3TeR4piBT4gTeo9kgL0HMbieqpjdfRrwUavNpWIcAzzm7o3uvgxYQhyrnaZYvO4+\n2d2bkptvAIOSn6sebxJfsdcY4O/Ada22VTzmSiTszE2qSVpUw4g3zAB3X5PsWgMMqFJYpYwDrgWa\nCralOeYGYJ2ZPWhmb5vZvWbWkxTH7O4bgduB94lE/bG7TybFMRcoFeNA4ljMS+NxeTHwfPJzauM1\nszHACnd/p9WuisdciYSdqVFMM+sFPAVc5e6fFu7zGJFNzd9jZj8E1rr7TJpb1y2kLWaiEmk4MMHd\nhwNbaNWVkLaYzewI4GqgnjgIe5nZBYX3SVvMxexFjKmJ38xuBHa4+6Nt3K3q8ZpZD+AG4KbCzW38\nSofGXImE/SFQV3C7jpZnndQws65Esn7E3Z9JNq8xs4OT/YcAa6sVXxHfBM41s6XAY8D3zOwR0h3z\nCqI18mZy+0kiga9OccwnAa+5+wZ33wk8DZxKumPOK/VeaH1cDkq2VZ2Z/ZLo5vt5wea0xnsEcSKf\nnRyHg4AZZjaAToi5Egn7LWCImdWbWTeiE35iBZ6nXczMgPuB+e5+R8GuicBFyc8XAc+0/t1qcfcb\n3L3O3RuIQbCX3P0XpDvm1cAHZnZksukMYB7wHCmNmRgUPcXM9k/eJ2cQg7xpjjmv1HthIjDWzLqZ\nWQMwhJjwVlVmNpro4hvj7tsKdqUyXnef4+4D3L0hOQ5XEIPTa+iMmN29w7+As4mZkEuA6yvxHB0Q\n42lEP/AsYGbyNRroC7xIjFhPAvpUO9YS8X8HmJj8nOqYgROAN4HZRGu1dwZivo44scwhBu+6pi1m\n4lPWSmAHMW70q7ZiJD7KLyFOSGelIN6LgcVEpUX+GJyQlnhbxbw9/xq32v8e0LezYtbEGRGRjNAl\nwkREMkIJW0QkI5SwRUQyQglbRCQjlLBFRDJCCVtEJCOUsEVEMkIJW0QkI/4P3voepXlllKEAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f166c6cd7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dataset area plot\n",
    "iris_df.plot(kind='area')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f166c573590>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rVpnfp6WlnXHNzp07+b//+z8++eQTsrOzyc/PN88+GDVqFI8//jjjx4+nuLjY\nPJVMSsmnn37K/PnzOXHiBFVVVWZl1pht27bRsWNHPDxO3zqnTp3K5s2b+e2338jPz+fVV19t4IJa\nv349mZmZLFy4kMmTJzNz5kxWrlzJjh07+O9//8vq1avN53br1o2srKwmh/HojVIICrdBSsmJ0hPn\nhIUg0tPt8mrV3i4yQjM1NdWsANasWcP06dPN71evXt1gqL2JL7/8kjFjxjBs2DC8vb35xz/+0eDm\nLU93UG7w/d5xxx2kpKTQvn17rr/+eqvHZdbW1jJv3jzeeustYmJi8PDwYPDgwXh7e5vPeeqpp/D2\n9ubSSy8lMDCQG2+8kfDwcGJjYxk+fHiDcZmmtR0xLtMSqtupwm0orirG08MTPy+/Vq8R5R9FRl6G\nHaXSB2nh6deRNDdC86OPPuLf//63+Xh1dXWzIzQff/xxvvzyS3Jzc80357y8vDPmEDfmoosuYurU\nqRw7dgyj0ci4ceOYMWMGBw8epKioiPPOO++MaxqPy/Tz8yMsLKzF77f+jGVbxmXm5eVRUVFht3GZ\nprUdMS7TEspCULgNbUk5NREdEM2xUte3EJyNK4zQTElJwc/Pj3//+9+kpqYSGBhIdHQ0c+bMYfjw\n4RaviY2N5fDhw+b3ZWVlDeIBbc1o6tOnDwcOHKC2thbQhu+0b9/ebuMyd+3aRXJyMgEBAXZZz1aU\nQlC4DW1JOTWhsoxaRrrQCM3U1FTefvtts3soLS2twfvG/PWvf2XJkiX8+uuvVFVV8fTTT5tv3qBZ\nAllZWWfsa22mU3x8PCkpKaxbtw4ADw8P7rjjDqZMmUJOTg5Go5HffvvNPMnNVlatWsUVV1zRqmvt\ngVIICrfBXhaCCio3j6uM0ARNIZSUlHDRRRdZfN94jZ49e/LOO+9w4403EhsbS2hoaAP317hx4wAI\nCwvj/PPPb7CGtTI1Hpf52muv0bt3bwYOHEhYWBjTp083KxhrLJL65yxcuJCJEye2eI1eqHkICrfh\ng80fsPrgauZfM7/VaxRVFBH/RjzF01sOauqJK89D6NChA++//z4XX3yxs0VxSaqqqujXrx8rV660\na3Ha4sWL+eSTT1i4cKHN19prHoIKKivcBntYCEE+QdTU1lBaVYq/t7+dJFOcS3h7e7Njxw67rztm\nzBjGjBlj93VtQbmMFG6DPWIIqn2FQtE0ykJQuA25Zbn0jOjZ5nVMtQgdDR3tINXZhykTSHHuoSwE\nhdvQ1rYM9tRZAAAgAElEQVQVJuKC4jh66qgdJFIozi6UQlC4DW1tW2EiLjCOI6eO2EEiheLsQleF\nIIQYJYTIEELsFUI81sQ5aUKIzUKI7UKIdD3lUbg39rIQ4oPiOVqsLASFojG6xRCEEO2At4GRwFFg\ngxBikZRyV71zQoB3gMullEeEEOF6yaNwf+xpIWw+trnlE3WmrVWzCoW90TOoPAjIlFJmAQghFgJ/\nAXbVO+dG4H9SyiMAUso8HeVRuDGlVaXUyloCvNte0h8fFO90l5Gr1iAozm30dBnFAYfrvT9S91l9\nOgOhQoifhRB/CCH0mTqhcHuOlx4nyj/KLk/VKqisUFhGTwvBmkcgL6A/cAngB/wmhPhdSrlXR7kU\nbsixkmNEB0S3fKIVxAXGkV2cjZRSuW0UinroqRCOAgn13iegWQn1OQzkSSnLgXIhxGqgL3CGQpgx\nY4b567S0NIvDMRRnL8dLjttNIfh6+eLv7U9eWZ5dgtQKhauQnp5uHirUGnTrZSSE8AR2oz39ZwPr\ngQmNgsrd0ALPlwM+wDrgBinlzkZrqV5G5zizNsziz2N/MnvMbLus12dWHz4a+xHnRZ/ZU1+hOFuw\ntZeRbjEEKWUNMAn4EdgJfC6l3CWEmCiEmFh3TgawFNiKpgzmNlYGCgVoMQR7WQjgGoFlhcLV0LV1\nhZTyB+CHRp/NbvT+NcDyAFOFoo5jJcfoE9XHbuvFBarAskLRGFWprHAL7BlUBmUhKBSWaFEhCCG+\nEkJcKYRQykPhNOztMooLilPVygpFI6y5yc8CbgIyhRAvCSG66iyTQnEGx0qOEeVvv2Ekqn2FQnEm\nLSoEKeVyKeWNaPUCWcAKIcRaIcTtQggvvQVUKKSUmkIIsJ9CUA3uFIozscoNJIQIA24D7gI2Af8C\nBgDLdZNMoaijuKoYTw9Pu7StMKGqlRWKM2kxy0gI8TXQDVgAjJFS5tQdWiiE2KincAoF2N9dBGBo\nb6DKWEVJVYldFY1C4c5Yk3Y6V0r5ff0PhBA+UspKKeUAneRSKMzYs0rZhBDCbCV0DVdhMYUCrHMZ\nvWDhs9/sLYhC0RT2jh+YUIFlhaIhTVoIQogYIBbwFUL0BwRaw7ogtEZ0CoVDOFZyjGh/+1oIoALL\nCkVjmnMZXQ7citay+p/1Pi8GHtdTKIWiPvauQTARHxSvAssKRT2aVAhSyvnAfCHEX6WU/3OcSApF\nQ46VHGNQ3CC7rxsXGEdGXobd11Uo3JXmXEY3SykXAMlCiCn1DwFSSvm67tIpFMDR4qPEBsbafd24\noDhWHFhh93UVCnelOZeRKU4QSMNhNwLrht8oFHbh6KmjxAU2HrbXdlRQWaFoSHMuo9l1/85wmDQK\nhQWOFh8lLkgfhXC46HDLJyoU5wjWNLd7RQgRJITwEkKsEELkqdnHCkdRXl1OSVUJ4X7hdl87yj+K\ngooCKmsq7b62QuGOWFOHcLmU8hRwFVovo07AI3oKpVCYyC7OJiYgBg8dmu2282hHTECMchspFHVY\n81dmcitdBXwppSxCxRAUDkIvd5GJhOAE5TZSKOqwpnXFYiFEBlAB3CeEiKz7WqHQnaOnjhIfFK/b\n+glBCRw+pRSCQgHWtb+eBgwFBkgpq4BS4C96C6ZQQJ2FoEOGkYnE4EQOFR3SbX2Fwp2wdqZyNyCp\n3vwDCXykj0gKxWkcYSFsP7Fdt/UVCnfCmiyjj4FXgWHA+XWvgTrLpVAAcKT4iP4xBOUyUigA6yyE\nAUAPKaUKJJ+DlBqNzMvJIauighEGA1eEhiKEcNj+ehWlmVAuI4XiNNZkGW0HYvQWROF65FVVMXjT\nJlYUFhLm5cW0/fu5dscOyoxGh8mge5aRCiorFGasUQgRwE4hxDIhxOK61yK9BVM4FyklE3btYnRo\nKF/36sX0pCQ2DhhAYLt2/GX7dqpra3WXoVbWklOco0sfIxOhvqFU1lRSXFms2x4KhbtgjctoRt2/\nEq2PkelrxVnM5ydOkFtVxcwOHcyfeXt48EHXrlyzfTtT9u3j35076ypDbmkuQT5BtPdsr9seQggS\ngxM5fOowPSJ66LaPQuEOWJN2mo5WoexV9/V6YLOuUimcSq2UPJ2VxRspKXh6NPwV8fTw4OPu3Vmc\nl8f3J0/qKofe7iITqjhNodCwJsvoHuALYHbdR/HA13oKpXAu3508SbCnJ2khIRaPh3h58WH37ty1\nezf51dW6yXGo6BAJQQm6rW8iIShBBZYVCqyLIdyPlnJ6CkBKuQeI1FMohXN5LzubB+Pims0mSg0J\nYWx4OE8cOKCbHAcLD5IUnKTb+iZMLiOF4lzHGoVQKaU0t4MUQniiYghnLXlVVawpKmJseMvdRZ/v\n0IFv8vJYf+qULrIcLDpIckiyLmvXR2UaKRQa1iiEVUKIJwA/IcSlaO6jxfqKpcgoLeUfWVkcKC93\n6L5f5uYyOjSUAM+W8w0MXl680rEj9+3Zg1GHMpWDRQdJCtHfQkgIVi4jhQKsUwjTgFxgGzAR+B54\nUk+hznVOVFVx8ZYt7CkvZ8Sff1Koo5++MV/m5nJDpPUewb9FReHr4cFHx47ZXRaHuoxUUFmhsCrL\nyAh8A/yflPI6KeVcVbWsLy8dOsR1EREs6N6dEQYDrx854pB9S2pqWFdczKUGg9XXCCF4rVMnnjpw\nwO4Faw6zEOpcRurXWnGu06RCEBozhBB5wG5gd920tGeEI3sXnGNU1tYy/9gxHknQsmumJSYyJzub\nGgcUgq0sLGRQYKBV7qL6DA4OZmhwMK8ftt9TdmlVKSVVJUT665+/4O/tj6+nL3llebrvpVC4Ms1Z\nCA+jtb0eKKU0SCkNwKC6zx52hHDnIj/m59Pb35+E9loxVlc/Pzr4+rKsoED3vZfm5zM6NLRV177Y\nsSNvHDnC8aoqu8hiSjnVY1KaJVSmkULRvEK4BbhRSmnOK5RS7gduqjum0IGv8/IYFxHR4LO/hoez\nWOciMNCU0eWtVAgdfX25NTqaZ+yUhuood5EJVZymUDSvEDyllLmNP6z7zDafgsJqfi4oYGQjH/7o\nsDB+OHlSVx/3kYoKThmN9PL3b/UaTyYl8WVuLvvskBnlqICyCVWcplA0rxCaS22xKu1FCDFKCJEh\nhNgrhHismfMGCiFqhBDXWrPu2UpWeTkVtbV09fNr8HkPPz9qgd1lZbrt/UtREcOCg9vU2jrUy4tJ\ncXH8IyurzfJkFWY5pAbBhHIZKRTNK4Q+QohiSy+gd0sLCyHaAW8Do4AewAQhRPcmznsZWMrp5nnn\nJKuKikgNCTnjpiyEIDUkhDVFRbrt/UtREcODg9u8zkPx8XyXn8/eNiqvg0WOtxCUQlCc6zSpEKSU\n7aSUgU28rHEZDQIypZRZUspqYCGWZzE/AHyJVutwTrO27indEhcGBbFWp4pgsJ9CCPHyYnJcHM8d\nPNimdZwRQ1AuI8W5jp4pHHFA/UeuI3WfmRFCxKEpiVl1H53TieCbSkroHxho8diFwcGs1clCyK+u\n5mBFBf0CAuyy3oPx8fyYn8+u0tJWr+Fol1FScBIHC9umxBQKd0dPhWDNzf1NYFpdoZvgHHYZVdfW\nsrO0lL5NBHV7+fuTU1VFnp3SOuvza1ERFwQFndHqurUEeXrycHw8Mw+17om7rLqM/PJ84oPi7SKP\nNcQHxZNXlkdFTYXD9lQoXA09s4WOAvV7FyegWQn1GQAsrPOZhwOjhRDVUsozJrLNmDHD/HVaWhpp\naWl2Fte5ZJSVkeDj02RRWDshGBgYyLriYq4MC7Pr3uuLixkSFGTXNe+LjaXjunUcrqgw11RYy/6C\n/SSHJDusBgGgnUc7EoITOFh4kK7hXR22r6OprISNG2H9ejhyBE6cACnBxweioiAhAZKToVcviIsD\nVYLqXqSnp5Oent7q6/VUCH8AnYUQyUA2cAMwof4JUsqOpq+FEPOAxZaUATRUCGcjzbmLTPQPDGSz\nDgphw6lT/F+cfQfRhHh5cVt0NG8dOcJrKSk2Xbsvfx+dDJ3sKo81dDR0ZH/B/rNKIWRnazf/tWu1\n159/QteuMHiwduPv3Vu76VdWQk4ObNoEX3wBO3ZARYWmGHr1ggsugNRU6NBBKQlXpvHD8rPPPmvT\n9bopBClljRBiEvAj0A54X0q5Swgxse747GYXOMfYXFxM/xZ8+P0CAvgy176xdyklfxQXc34Lyqg1\nTI6Pp/8ff/BUcjLBNrTDyMzPJCXUNiViDzqEdGB/wX6H79sWamth61bYuRMOHYKjR7VXdrb2vqoK\nBg3SFMCzz2o3dmtDRbm5mmLYtg2WLYPHHwd/f7jlFpg4UbMoFGcXuhaYSSl/AH5o9JlFRSClvF1P\nWVydLaWlLT759wsIsPtAmqyKCnw8PIj18bHrugBJ7dszKjSUOdnZPJKYaPV1+wr20T38jAxl3elo\n6MiBQv0G/tiT0lJ4/XV45x0IDoZ+/SAxETp31p7kY2MhPl5zAbX2iT4iAtLStNcDD2iupY0b4T//\ngR494KGHYNo08PKy53emcCaq4thF2FtWdkZBWmM6+/lxoqqKwupqQuz0V6iXdWDi4fh4rtuxg78n\nJOBh5Z1pX8E+rupylW4yNUVHQ0d+P/K7w/e1lb17YcwY6NsXfv4ZujtIdwoB55+vvaZP16yE1FT4\n6iuIjnaMDAp9cVzUTtEkZUYjJ2tqiG/hKb2dEPQNCODPkhK77f1HcTEDdVQI5wcFEeblxbL8fKuv\ncZbLyBRDcGX274cRI2DKFPj8c8cpg8YkJcH338Pll8Pw4Zp7SuH+KIXgAmSWl9OxfXurnqD7BQSw\n2Y4KYYPOFgLAxNhYZufkWHVutbGaI6eOOLQGwYRJIbjqXISKCrjuOnjkEbjnHmdLAx4e8MwzmqVw\n5ZWgY92kwkEoheAC7C0vp7Ovr1Xn9gsMtJuFUCslGx2gECZERrKqsJDsysoWzz1UdIjYwFi823nr\nKpMlQtqH4Onhycly/TvLtoZnnoFOneDBB50tSUP+/nfNSrjxRi3OoHBflEJwATLLy+ncQvzARF9/\nf7bYSSFklpcT6uVFuLe+N99AT0+uj4jgAyushMz8TKeknJpwVbfR7t3wwQfw9tuul/YpBLz1Fhw/\nDu+952xpFG1BKQQXYG9ZGSlWWgg9/f3ZXV5OlR0mqDnCXWTi9pgYFhw/3qI7Zl+Bc2oQTHQ0dCQz\nP9Np+zfFY49pgVxXTfX08oIFC+Cpp7Q4h8I9UQrBBbDFZeTbrh0d2rdnlx1aYesdUK7PoMBAjFKy\nqQXrZl/+PqcElE10C+9GRl6G0/a3xLZtsG4d3HefsyVpnm7dNPfRlCnOlkTRWpRCcAFsUQgAfQMC\n7OI20jvltD5CCG6MiuKT48ebPS+zIJNOoc6zELqHd3c5hfDii/Dww2DDr4jTePjh04VsCvdDKQQn\nU2o0UlhTQ5wNhWH2iCMYpeTPkpIWq6PtyY2RkSw8cQJjM26jPSf30CWsi8Nkaky38G7sytvltP0b\nc+wY/PCDlsnjDrRvD6++qrm4VIDZ/VAKwcnYknJq4jw7WAi7y8qI9va2W4GbNXTz9yfG25ufCwos\nHq82VnOg4IBTXUZdwrqQmZ9JTW2N02Soz/z58Ne/atXI7sLYsdq/iyx2JVO4MkohOJm9ZWVWZxiZ\nMBWntSVffqMVvZP0YHxkZJP9mA4UHiAuKI72nrZ1R7Un/t7+RPlHkVWY5TQZTNTWwty57mMdmBAC\nZszQXspKcC+UQnAytsYPAKK9vfEQguw2zEbYWFzMAAfFD+pzTXg43548Sa2FO0VGXgZdw5zfabRb\neDd25TrfbZSeDoGBWqsId+PqqzXF8N13zpZEYQtKITiZzPJyq1NOTYi6FhZtcRttLClxikLo7OdH\nmKcn6yyUte7O20238G4Ol6kxrhJYXrgQbrrJ9eoOrEEILePozTedLYnCFpRCcDKtsRCgbYHlWicE\nlOtzTXg43+TlnfH57pO7XcZC2Jm306kyVFfD11/DuHFOFaNNjBsHu3Zp7bkV7oFSCE6m1QqhDRbC\nnrIyIry8MDipb/HYiAi+zss7IwaSkZfhEsNp+kT1Yetx597FVq7U2lQkJztVjDbh7Q3336+sBHdC\nKQQnUlxTQ1FNTatmEfQNCGBLK4fYO8tdZKJ/QADltbVnFNftPukaLqM+UX3YlbuLKqP951dby+ef\nww03OG17u3HPPZqlY8EgVLggSiE4kX3l5XTy9bUp5dRENz8/sioqKDMabb52Y3ExA5zkLgItBnJ1\nWBjfnTzdRO5k2UmqjFVE+Tu/N4O/tz8dDB3Ymesct1F1NXz7rdbZ1N0JD9dmNyxY4GxJFNagFIIT\naa27CMDbw4Nufn5sb4WVsKm4uMX5zXozKjSUpfVmJJjiB8JFIqj9Y/qzKWeTU/Zeu1abXZyQ4JTt\n7c5dd2npsyoF1fVRCsGJtEUhQOsCy7VSstnJLiOAESEhrC8upqRGKwBzlQwjE/2i+7E5Z7NT9l66\nFEaPdsrWujB8uFZTsXatsyVRtIRSCE4ks60KoRWB5czycgyenoQ5eRBugKcnAwMDSS8sBFynBsFE\n/5j+bMzZ6JS9ly6FUaOcsrUuCHHaSlC4NkohOJG9rahBqE9rAsvOKkizxOX13EauElA20T+mP1uP\nb3V4YDknB7Ky4IILHLqt7txyC3zzDdTpf4WLohSCE2lN24r6mCwES1W/TeHIGQgtMSo0lB/r+hq5\nSsqpiSCfILqEdXF4HGHZMhg5Ejw9Hbqt7kRGwiWXwBdfOFsSRXMoheAkTtXUUGw0EtuGaWVhXl4E\ntWtHVkWF1df8duoUQ4KCWr2nPenj70+J0ciuklNkFWY5tamdJYYlDmPNoTUO3fNscxfV5+ab4aOP\nnC2FojmUQnASppTTtmbV2BJHqKytZWtJictYCEIILjMY+Dx7n9Ob2lnC0QrBaITly+Hyyx22pUO5\n4gqtcvnAAWdLomgKpRCcRFszjEzY0gp7c3ExXfz8CHAhf8SIkBCW5+e6VEDZxNCEoaw5tIZa2fZx\npdbwxx8QEwPx8Q7ZzuF4e2vFdh9/7GxJFE2hFIKTsJdCsCWw/PupUwx2EXeRiREGA1sqBD0iejpb\nlDOIC4ojyCfIYY3uzmZ3kYmbb9aK1FRNgmuiFIKTaGtA2YRpNoI1uFL8wERS+/YIYzkhYec5WxSL\nXJR0EasPrnbIXueCQjBlT61f71w5FJZRCsFJtKbttSVSfH05UVVFUU3LE75+c0ELAcC7eCeF7Ts4\nWwyLpCalsurgKt33OXkSduyAYcN038qpCAF/+5tqZeGquI4z+RzDXi6jdkLQq65i+aKQkCbP219e\nTrWUdtnTnhhrjRSfWM2ejq75aJyWnMbjKx9HSqlrW42flktuHLAHn/+uh4MH4cQJ7e7Zvr3W8rRr\nV+3x2t9fNxkcxd/+pn0rr7+uxRUUroOyEJzAqZoaSo1GYuz01zAkKIhfi4qaPWdlQQEXh4S4TK8g\nE/sL9hNZlc2vp2yrp3AUySHJeHl4sefkHn02WLcO7r+fUbdH88rWy7URY2Vl0LGj9goJgc2b4amn\nICoKUlPhvfegibnU7kDHjpp+W7rU2ZIoGqMsBCdgqlC21805LSSE97KzmZ6U1OQ5KwsLucRgsMt+\n9mRn7k76hsaR6eXF1pISznORlFgTQgjSktNYdXCVfQvnli2D55+HI0eQt9/B5QFr+eT3TgR1auaa\n0lJtUMKCBTB9ulb++8gjbpmWZAouX321syVR1EdZCE7AXvEDExeFhLD21Cmqay2nR0opWVlQwCXN\nuJScxY7cHfQI78HFBgM/u2hfg7TkNNKz0u2z2L59Wj/oBx6A++6DPXvYevWTnAzpRKfmlAFo7qIx\nY+C//4WdO8HLC/r00ZSChZGkrsz112s60Y0NnbMSpRCcgL0yjEyEennRoX17NhYXWzy+rbQU/3bt\nSHax+AFoCqFnZE9GhISw0kUVQmpSKulZ6WdMeLMJKWH2bM15PnSoNldywgTw9GxddlFMDLz2mlbp\nlZcH3btrisJNMBjg0ktVKwtXQykEJ2CvgHJ9LjUYGswXqM/XeXlcEx5u1/3sxc7cnfSM6ElaSAhr\nioowumAcoaOhI+082pGZn9m6BQoL4dprNd//mjUwbRrUm5LXpnTTqCiYNw++/FKLM/ztb27TQe6W\nW1S2kauhFIITaGuXU0tcEx7O103MKfwqN5exLqgQjLVGduftpntEdyK9vYnx9m71nGg9McURWuU2\n2rcPhgyBuDj4/Xfo1rCja3GxVqGcltZGIYcMgU2bICgI+vbVgtUuzqhRkJEB+/c7WxKFCaUQnEBb\n5yBYYkhwMMeqqshsNKd4R2kpudXVDAkOtut+9mB/wX4i/SMJ8NbGeaaFhJjnI7gaqUmppB9Mt+2i\nNWs099ADD8DbbzewCkysXAmDB9spm9TfH959F/71Ly3W8MEHdlhUP7y9Yfx41crCldBdIQghRgkh\nMoQQe4UQj1k4fpMQYosQYqsQ4lchRB+9ZXImRTU1lBmNRNs5AbudEIyPjOSDY8cafP5edjZ3xsTQ\nzsXSTeF0/MCEKyuEtOQ0VmWtsj6O8MMPmpvoww/h//6vydN0qU7+y19g9Wp4+WWYNEkb0uyimDqg\nuqCn8JxEV4UghGgHvA2MAnoAE4QQ3Rudth+4SErZB/gHMEdPmZzN3rIyuvj56VIPMCkujrk5Oeax\nlMerqvj0+HHuiYmx+172YGfuTnqE9zC/T3XhOEInQyckkn0F+1o+edEiuPVW+PbbZluXSqlju4pu\n3bT+EPv2wTXXaCmrLsjAgdrsh99/d7YkCtDfQhgEZEops6SU1cBC4C/1T5BS/ialNFVVrQPcL6na\nBvaUl9NFp2yfzn5+XBEayqP792OUksl793JbdDQJ7V2rrbSJxhZClLc3Ud7ebHXhOMKqrBbaWPzv\nf3DPPfD995pfvxn27oWaGujRo9nTWk9wsKacIiK06TRNxJiciRBqToIrobdCiAMO13t/pO6zprgT\n+F5XiZzMnjoLQS/eSEnht1OniFm7lhPV1TzfoY09gioq4PBhrdmOnZ/cd5zYQc9GXU5d2m2UlNZ8\nHOH77zX30NKlcP75La5nsg509eZ5eWlZSBdfrMUzsrJ03Kx1/O1vWvppZaWzJVHoXals9R1ECDEC\nuAMYaun4jBkzzF+npaWR1ua0DOewp7ycK0JDdVs/1MuLPwYMIKuigg7t2+PRmrvN0aMwZ442BDcj\nA8LDtXYK7dppN5bbb2/zncxYa2TPyT10j2joQUwLCeHT48d5OCGh1WvrRWpyKs+tfs5yX6M1azQ3\n0aJFcJ51nVt/+AHuvFMHQRsjBMycqaWopqXBihW0XAXnOJKSoFcvrWvHtdc6Wxr3Jj09nfT09NYv\nIKXU7QUMBpbWez8deMzCeX2ATCCliXXk2cKADRvkuqIiZ4thmdJSKZ96SsrQUCnvv1/KtWulrK4+\nffzIESlnz5ayb18pBw+W8vffW73V7rzdMvnN5DM+z6mokIZffpE1tbWtXlsvamtrZcxrMXJf/r6G\nB7ZskTIiQsqlS61eq7RUysBAKQsL7SxkS8yaJWVCgpR79jh44+Z5/30pr7nG2VKcfdTdO62+Z+vt\nMvoD6CyESBZCeAM3AIvqnyCESAS+Av4mpWxl5Y97IKVkjw4pp3YhI0OL8O3aBVu2aGmSQ4Y0nPYe\nF6f5xzdt0tou/OUvWj8eo9Hm7bYc20LfqL5nfB7t40OUtzfbXDiO0KAeISsLRo+Gf//bptmX6enQ\nr5/m5nco994LTz8NI0bA7t0O3rxprrsOfv4ZcnOdLcm5ja4KQUpZA0wCfgR2Ap9LKXcJISYKISbW\nnfY0YABmCSE2CyHO2tEZx6uqaO/hgcHLy9miNOSnn+Cii+Dhh7X2By01S/Pw0MpMN27Urr32Ws2l\nZANbj2+lT5TlDOPU4GCXjSOY2lgAWv+gMWNg6lRtNqQN/PCDpkecwl13wQsvaO6/XbucJERDgoK0\nZKj5850tyTmOLeaEs16cJS6jVQUFcujGjc4WoyGLFmnujtWrW3d9ZaWUN9+suZAKCqy+7OrPrpZf\n7PjC4rHPjh2Tf9m6tXXy6ExGboZMfCNR1lZVSTl6tJQTJ0ppo3urtlbKjh01T5NT+egjKePipNy7\n18mCaPz+u5SdOklpNDpbkrMHXMxlpKiH3hlGNvPDD9rT4nffwfDhrVvD21srvho4UHvkbaLBXmOa\ntRBCQlhdVOSS8xG6hHWhsqaS4gcnQlWV5iqyMbi+d6+WUdO7t05CWsvNN2vuo5Ej4dAhJwsDgwZB\nYKBmdCqcg1IIDkTPGgSb+eMPze3zzTfazbwtCAFvvaW1Yr7qKi1VtRmKKorILc2lk8FypkuMjw+R\ndfMRXA0hBM9lxCCXLtVyJVvh/jO5i1yiePyee+Chh7Q6hZwcp4oihBbieO89p4pxTqMUggNxGQvh\nwAFtMsncuS0WT1mNEDBrFkRHwx13NFuzsO3ENnpG9qSdR7smz0kLCWFVC1PgnMLy5dz09T7+OT1N\n6+HcCr7/3onxA0s89JCWMjtypNOL1268UQu4Hz3qVDHOWZRCcCC7XcFCqKqCceO0oSrXXGPftT08\ntKjg/v1Qr26kMVuPb6VPZPMtq1JdsUBt1y646SYOz3mVr43bWrVEaSmsXavde12KJ57QHhIuu8yp\n7bMDA+Gmm7QkN4XjUQrBQVTW1pJVUeF8C+HJJyE2Vnsq1ANfX62Hz0cfNdnGcuvxrfSNPjPltD6p\nISGsLix0nThCXp7mDnv5ZVLG3klWYRYF5baP+1q5UitiDgrSQca2YCpeGz4crrgCnOiumzJFM17d\nbAjcWYFSCA5id1kZHdu3x9vDiT/y5cvh00+1tsh6OrCjomDxYi2N9c8/zzjcXEDZRKyPD+FeXmxz\nhaZslZVaau24cXD77Xh6eDIobhBrD6+1ealvv9XKN1wSIeCNN7TmSldfDeXlThGjQwdtmtrcuU7Z\n/ih0VvMAABZNSURBVJxGKQQHsaO0lJ52aXrfSnJz4bbbtIwgRwzL6dVL68v/1782GJxbK2vZdmIb\nvSNbTrFJCwlhlbPdRlLCxIkQFqY9QdcxLGEYvx7+1aaljEats4W9PXV2xcNDG/UZHa1Vi1VVOUWM\nRx7RdJOTtj9nUQrBQWwvLaWXsxSClFr/oZtv1rJJHMWECVrh1s03Q20tAAcKDhDqG4rBt+WArEvE\nEV56CbZt09xf9ay7YYnDWHNojU1LrV2rFXsnJ9tZRnvTrp324ODlpUV569qpO5L+/TVDRRWqORal\nEBzEdmdaCG+/DSdOwD/+4fi9X31VC1K+8AIAm49tttiywhKpdRaC0+IIX36pTSBbtOiMkWaD4wez\nKWcTlTXWt+j8+msXtw7q4+UFn3+uxRLuuMOs0B3J88/Dc8/ZXASvaANKITiIHc6yELZu1f6qPv20\nVTnzbcbLS8vXf+89WLqUP7L/YGCsdXUPcT4+hHl5sd0ZcYQNG7R+Td9+qz3WNyLQJ5Cu4V3ZmLPR\nquWk1Eo+xo61t6A64uMDX30FBw9qbb0drJgHDdLGi/7rXw7d9pxGKQQHUGY0kl1VRSdHD6opK9OG\n1v7zn5CS4ti96xMTAwsXwq23cvTPXzg/tuVZASacMh/h8GHtUX7uXM130QTDEqx3G23dqv3r9Opk\nW/HzgyVLYPNmrWeTg5XCCy/Aa685vTzinEEpBAewq6yMLr6+eDo6w2jKFK2l5s03O3ZfSwwfjnz8\ncR59/XcGhDSeoto0Dg8sFxdrcY+HHmrRv2NLHOGrr7TlXKI62VYCA7VpPitWNFtfogddu2oDdB55\nxKHbnrMoheAAtpSUON5d9PXXWprprFkucxfa/7cr2RvTnsiHn7T6SdOhcYSqKi0ratAg7Wm4BYYm\nDuXXw79SK5v3r0upGUjjx9tLUCdgMMCyZVo33FdecejW//iHpot+/tmh256TKIXgADYVFzMgMNBx\nGx45ojWF+eQTl6qA+iNnI/+dfAls3251KWqcjw8GLy926B1HqK3V0nL9/LRAshVKNDYwFkN7A9tP\nbG/2vE2btJTTtraMcjqRkVrnudmzHVpKHBgI77yjTZdzdtLZ2Y5SCA5gY0mJ4xSC0ajZ2JMnaxE5\nF+KP7D/o02Gw5j95/nn45RerrksLCWGlnncCKTX32uHD8NlnDYcCtcDlnS5naebSZs/59FMte9NF\nDLW2ERenPa6/8opDu9CNGaMVUN91l8PDGOcUSiHoTE1tLdtKSugXEOCYDV96SbvzPPaYY/azgT9y\n/tACyh07agnm48drN+EWGB0ayvcnT+on2MyZ2k1u0SKt9YYNjO48ulmFYDRqOmbChLYK6UIkJ2v+\nm5decmgK0GuvaX0ZHeyxOqdQCkFndpWVEe/jQ6ANT52t5rfftP78H3+sFRe5ENXGajZmbzydcjp6\ntBa4vfJKaKGr6aUGA2tPnaJYjwKpl17SirB+/LFV3UvTktPYkL2B4krLcyBWrdKKfrtbH0d3Dzp1\n0r65t97Sak0cQPv2Whbwu+/CggUO2fKcQykEndlYXEx/R7iLCgu1NpGzZ1vMm3c2fx77k+SQ5IYV\nylOnaqM7//rXZnsUBHp6MiQoiJ8KbG8m1ywvvaT1dUpP1xr+tYIA7wAuiLuAFQdWWDz+0Ufaf8tZ\nSVKSphT+8x/NBegA4uO1eRKPPqrpcYV9UQpBZ9YXFzNQb4UgpeZcveIKl+2ctubQGoYlDmv4oWmw\njr+/FjFsphr2qrAwFtvLbSSllrrywQea66OVysDEmC5j+CbjmzM+LyjQitFuuaVNy7s28fGaQv3s\nM5g2zSEO/h49tP+2p5+Gl19WMQV7ohSCzqwpKmJYcLC+m8yapc0geO01ffdpA2sOW1AIoLm2PvtM\ny4y6807N6W6Bq8LC+O7kybann9bUaBXIX32l3cjsYE1d1+M6Fu1edEYbi08+gVGjICKizVu4NjEx\nmqWQnq71zKqu1n3Lbt1gzRqtCH7cuBa9jgorUQpBRwqqq8mqqNA3oLx5MzzzjNZ3xtGV0FYipWTN\noTUMT2xibrOpGvbgQU0pWIgVdPT1JdzLi3VtaZJfXKy1sT5wAFavbrNlYCIuKI4+UX0aBJelhDlz\ntAmV5wTh4VpgPi9Pa53tgHkKCQmaUoiIgAEDtG4jirahFIKO/FpUxKDAQP0qlE+dguuv1wLJnTvr\ns4cd2HNyD+0925MQnND0Sf7+mlLIydFuKBZu/NdHRvL5iROtE2L7dq0QIDpa28fObrzxvcbzybZP\nzO9//10bJzBihF23cW38/TUfWWys9o239v/KBtq31wzkF1/U8hNeecUpffjOGpRC0JE1RUUMDwnR\nZ/Ha2tPtrF28BHbZvmWM7GDFzEiTpZCYCEOHQkZGg8PjIyP5b24uRlvcRrW1WqB9xAiYPl17bNeh\nyd/4XuNZvn852cXZgNbL//77z5LaA1vw9NSCzFdeqVV8WxiQpAfjxmkWwqJFcPnl2nOFwnaUQtCR\n9MJChusVP3j6acjPd4tWkD/u+5FRKaOsO9nLS3vkmzQJhg3TrJ+6uEJXPz+ivb1ZbW2R2o4dmiIw\nZRLdemvrvgErCGkfwvie45mzcQ7792ujMu+6S7ftXBshtJ5Hr76qjT77/HOHbJuUpP03Dx2q9SRc\nssQh255dSCld/qWJ6V7kVlbKoNWrZYXRaP/FFy6UMilJyuPH7b+2nSmvLpeBMwNlflm+7Rfv3i3l\n0KFS9u0r5ZIlUhqN8pWDB+XdGRnNX7d1q5Q33SRlRISU//qXlDU1rRPeRrYf3y6jXo2S90wqltOn\nO2RL1+fPP6VMTpZy2jSH/T9IKeXq1VImJkr5wANSlpc7bFuXo+7eafW9VlkIOrGsoIARISH42Dt+\nsGYNPPCA5quNjLTv2jqw5tAaekb2tGpC2hl06aK1t3jqKe3VpQvj58/nf9nZlB47pkVupYSTJ7Vx\nZC+9pMUJRo/W0lD27dN+Vg4q0usZ2ZMh0SNYsOctHnjAIVu6Pn37wvr1mj/n4ou1bDIHMHy45q3K\nyYELLoC9ex2yrdujFIJOfH/yJKPDwuy76NatWhHXJ5/AeefZd22d+HrX14zpMqb1Cwihfc8bN8Kn\nn5JQWcmwXbv47MEHtRu9p6c26+GBB7S//uef17KVnnzS7oFja/Bf/w/k4DcQgcccvrfLEhGhVYJf\nfrmWDvTttw7Z1mDQmrPed59W/7h+vUO2dW9sMSec9cLNXEYVRqMM/eUXedieturevVLGxWnuIjeh\n2lgtI1+NlHtP7rXruktPnpT9NmyQtVVVUlZV2XXttrB/v5ShoVJOXjRdjl04VtbW1jpbJNfj1181\nd+fdd0tZWOiwbRcv1jyI33/vsC1dApTLyPkszc+nl78/8faqC8jIgLQ0LZB8ww32WdMBrD64mvig\neFJC7Tut7VKDgVM1NfxWVuacsaBNMG0aPPggvDT6aXaf3M28P+c5WyTX48ILYcsW8PCAXr1g8WKH\nbHvVVZphcvvtWqsvRRPYoj2c9cLNLIQbtm+Xs44c+f/2zj26qurO45/fvUFJCBiEoGhBEUyVBgUL\nA9qxXS1aMSBQRhkf05F5sGZVO6N0ybI47VT/mDXtACM404cUBB8FFYQuQEFxhC7ktWCAgCGAEJAg\njyBY07xJ7nf+2BdNwyMkOefe3Ov+rLVXznPv3znn5vz2b5/f77eDqaywUOrZU5o3L5j6Esj3F39f\n09ZNC6XuXx8+rLsLC0OpuzWsXCldd51UWenWd5XtUu5/5mrdoXXJFaw98957Ut++0vjx0kcfJaTJ\noiKpVy9pxoyENJd0aKGFkPSX/UUJmUIKoay2Vjlr1+qTIIYyli93du5rr7W9rgRzovKELvuPy/RJ\n5Seh1F/T0KBe69dr02efhVJ/S6isdMpgxYo/3758z3JdMfUKFR5rP4qr3VFZKf3sZ26s7ac/lSoq\nQm/y4EEpL0/6yU+kdB/Va6lC8ENGAfP8kSPcm5tLt7YMZUgwfTpMnOjs3PHjgxMwQczeOpsxN4yh\nW1bAH9bjXBqJ8FTv3vy4pORMpyFpPP443Hqry1vUmJF5I5k5YiZ3vXJXs7OqfWnJynIxC9u3O6+w\nvDwXe1JdHVqT11zjnPVWrHAfnM+TPuvLSUu0R7IKKWIhVNbXq+e6ddr5pz+1vpKjR6W775aGDHFd\nmRSkvKZcPab20M7jO0Nt53RDgwZu3qxXjh0LtZ0LMX++1K+fdCFDZcHOBeoxtYfe/+j9xAmWqmzZ\nIo0eLV11lfTss6FaDOXl0ne+I913n1RTE1ozSQVvISSP/yot5fbLLiO/NcnsYjE368egQc41b906\n15VJQWZsnMHwPsPJ75EfajsZkQi/ycvjif37OVpb2/wJAbN2rZupdOHCC09dfX/+/bw09iXGvjaW\nJcVLEidgKnLGLXX5cneDe/eGSZNCCSTo3BnefNNZCKNGnTN91pePlmiPZBVSwELYW1mpbmvXal9V\nVctP3rBBuu02afBgaePG4IVLIHs+2aNuv+imklMlCWvz6QMHdPvWraoLIyr8PGzYIPXoIb399sWf\ns+XjLeo5raee2/hceIKlGwcPuijn3Fxp+HDphRcCd1etr5cefdRZelu3Blp10qE9fVQGRgC7gQ+B\nJ89zzHPx/YXAoPMcE8rNCoqq+noN2bJFz5WWXvxJDQ3SqlXuR37NNdLs2W5bClNVV6Uhs4Zo5saZ\nCW23IRbT6B07NP6DD3Q6AfdwyRKpe3fpzTdbfm7JqRL1/2V/TVw6UTWn03ScIgyqq6XXX5fGjpW6\ndJHGjXPK4ciRwJpYsMA916lT21V4S5toNwoBiAL7gGuBDsB24MYmxxQAb8WXhwIbz1NXSLer7VTW\n12tkYaEeLCpSQ3MuC7GYVFwsPf20y+9y003S3LlavWpVYoQNkZrTNRr76lg9+MaDZwVkrV69OvT2\nq+vrNaKwUHdt3x6Mh9c5OHlS+sEPnP4+Y8i15trKa8o17rVxGvrboTrw6YEgRQycRDy7FnPqlDR3\nrnNX7dpVGjRImjzZaeoWfk9qen0ffih997tSfr4LYkt1L6SWKoQwvyH8BbBP0kFJp4FXgabzO44G\nXoy/8TcBOWZ2RYgyBcqW8nK+sW0bORkZzLvhBiJNcx3HYrB3r0s18cgjbmLyO++EEyfgjTecZ8WE\nCax5//3kXEBA7D+1nztevoOoRZkzeg7W5D6sWbMmdBk6RqMsy89nQHY2AzZvZs7Ro9QFlBj/8GF4\n5hmXHklycxINHer2tebaOl/amUX3LeLe/vcyeNZgpq2fRk19TSCyBk0inl2L6doVJkxwWVTLymDG\nDPdBYNYs95D69nWeec88A4sWQXHxeefsbnp9/frBypXO8enJJ90nvVmz3Lw/XwYyQqz7aqC00fph\nnBXQ3DFfAY6HKFerqY3F2FtVxYbychaWlVFUUcG/Z2cz4dNPsWXL3Iv+0CHYt8+VvXshJ8flhR86\n1H0sy89PiyT5FXUVrC9dz8KihSzevZgpfzmFScMmEY0kJpHcuciIRJjaty/35ebyVEkJT5WU8L3u\n3fl2167c3KkTfTIzm002WF0NBw+64PCtW+Hdd2HPHjflxB/+ADfeGIysZsYTtz3BmK+O4Ufv/Ijp\nG6bz8M0PMypvFAOvHEj2JSHOspdOZGS4REXf/KZbj8Xcw9u+3aU/f/ll9/fQITerW+/eX5Tu3d1D\nXrIEunVzpXNnLCuLvyroxLjvdWTFSmPePJg8GQYMcIHWgwfDdde50rVrWvw7f06YCuFincOb3s5z\nnzdyZHyvLq604Njf9+/PrKFDOR2JUH+OUhuNUpadTXlmJtceP86wXbv4x02bGL1jB5ldurjkXbm5\nX/zgCgpcV6NfP7ctCSzds5Tn/+95JBFTDBE3C4mvx5eb7m/u2PpYPUcrjlJRV8HXe36dgusLKH60\nmB6dgsu8KsE991z8oz67dEEayNWXV7Hyqyd5vc9xqnOrqM2pIVoXJVqTQaQ6g8jpCMQMNRj1dVBf\n65azOkKnbOh8E9z/7St579YeZGYGdnl/xvXdrmfZA8soKiti/s75PLbyMYpPFJPTMYfLMy8np2MO\nHaIdiFqUaCRKxCJELXqWFdYSHhrwEPfnt+9JlVpNJAL9+7vSmIYGl/zw0CGX/LC01HX7S0vhxRdd\nxtyTJ93Un1VVUFmJ1dZSkJlJQVYWsc4dqd3fgariKNW/zqC6PoPDdRkciEVRRoZTTNEM176ZUxIR\nI2Igs89fcoovKf78RKN9jbY5vnjGsrO3XXIpDLy5yfUvWABtmLLXdOblGTBmNgx4WtKI+PoUICbp\nF42O+Q2wRtKr8fXdwLckHW9SV3IjjzwejydFkXTRvYcwLYQtwPVmdi1wBPhr4IEmxywFfgi8Glcg\nf2yqDKBlF+TxeDye1hGaQpBUb2Y/BN7GeRzNkVRsZv8U3/+8pLfMrMDM9gGVwN+FJY/H4/F4Lkxo\nQ0Yej8fjSS1SJnWFmU01s2IzKzSzxWYW0uz1icPMRpjZbjP70MyeTLY8QWJmvcxstZkVmdkHZvYv\nyZYpDMwsambbzCwxif0TiJnlmNmi+P/drviwblpgZlPiv82dZjbfzC5NtkxtwcxeMLPjZraz0bbL\nzWyVme01s3fMLKe5elJGIQDvAF+TdDOwF5iSZHnahJlFgf/BRXP3Bx4ws4CcGtsFp4FJkr4GDAMe\nTbPrO8NjwC4u3qsulZiJCxy9EbgJKE6yPIEQ/645EbhF0gDckHaqu13Nxb1LGvNjYJWkPOB/4+sX\nJGUUgqRVks5EGm3CxSukMhcTuJeySDomaXt8uQL3MrkquVIFi5l9BRdtP5uz3adTmrgFfrukF8B9\nE5T0WZLFCopyXIcly8wygCzg4+SK1DYkrQU+bbL588Df+N+xzdWTMgqhCX8PvJVsIdrIuYLyrk6S\nLKES75ENwinydOJZYDIQTEh0+6IPcMLM5prZVjP7rZllJVuoIJB0CpgOHMJ5QP5R0rvJlSoUrmjk\ntXkcaDYLRLtSCPHxrp3nKPc0OuZfgTpJ85MoahCk4xDDWZhZNrAIeCxuKaQFZjYKKJO0jTSzDuJk\nALcAv5J0C84LsNkhh1TAzPoCj+PyrF0FZJvZQ0kVKmTO5DVq7rgw4xBajKQ7L7TfzCbgTPThCREo\nXD4GejVa74WzEtIGM+sAvAG8Iun3yZYnYG4DRptZAdAR6GJmL0n62yTLFRSHgcOSNsfXF5EmCgEY\nDKyXdBLAzBbjnufvkipV8Bw3syslHTOznkBZcye0KwvhQpjZCJx5PkZS+8wE1jI+D9wzs0twgXtL\nkyxTYJjLrTAH2CVpRrLlCRpJT0nqJakP7oPke2mkDJB0DCg1s7z4pjuAoiSKFCS7gWFmlhn/nd6B\ncwxIN5YCD8eXHwaa7ZS1KwuhGf4buARYFc/jskHSI8kVqfWcL3AvyWIFyTeAvwF2mNm2+LYpklYm\nUaYwScchwH8GfhfvsOwnTQJHJRWa2Uu4TlkM2ArMSq5UbcPMFgDfArqbWSnwb8DPgdfN7B+Ag0Cz\nk7P7wDSPx+PxACk0ZOTxeDyecPEKwePxeDyAVwgej8fjieMVgsfj8XgArxA8Ho/HE8crBI/H4/EA\nXiF4PB6PJ45XCB6Px+MB4P8Be5cSgwPel9cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1669e11150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dataset density plot\n",
    "iris_df.plot(kind='kde')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following uses [Principal Component Analysis (PCA)](https://en.wikipedia.org/wiki/Principal_component_analysis), converting the dataset's variables into a set of principal components, which will then be plotted in both 2 and 3 dimensions.\n",
    "\n",
    "This code has been taken in totality from Scikit-learn's official [Iris Dataset Documentation](http://scikit-learn.org/stable/auto_examples/datasets/plot_iris_dataset.html\n",
    ")."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ODTKNE4UCCSeCyBOJlgBJlEaLRqMIBoPCMha5MF1LxyMVRQDg8/k6pdGkqTWiuMilMd1o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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1669aaeb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dkc56eSbiIrZiaksbCIKATdGZMGveBRt+2FJuPG/3xlgUaIs+Hg4oUmnQa8cl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\n7du3T+Hh4Sf9a4CahTtIAQDgMRZIAQDgE8oWAAC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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1669b35910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "# import some data to play with\n",
    "X = iris.data[:, :2]  # we only take the first two features.\n",
    "Y = iris.target\n",
    "\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "\n",
    "plt.figure(2, figsize=(8, 6))\n",
    "plt.clf()\n",
    "\n",
    "# Plot the training points\n",
    "plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired)\n",
    "plt.xlabel('Sepal length')\n",
    "plt.ylabel('Sepal width')\n",
    "\n",
    "plt.xlim(x_min, x_max)\n",
    "plt.ylim(y_min, y_max)\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "\n",
    "# To getter a better understanding of interaction of the dimensions\n",
    "# plot the first three PCA dimensions\n",
    "fig = plt.figure(1, figsize=(8, 6))\n",
    "ax = Axes3D(fig, elev=-150, azim=110)\n",
    "X_reduced = PCA(n_components=3).fit_transform(iris.data)\n",
    "ax.scatter(X_reduced[:, 0], X_reduced[:, 1], X_reduced[:, 2], c=Y,\n",
    "           cmap=plt.cm.Paired)\n",
    "ax.set_title(\"First three PCA directions\")\n",
    "ax.set_xlabel(\"1st eigenvector\")\n",
    "ax.w_xaxis.set_ticklabels([])\n",
    "ax.set_ylabel(\"2nd eigenvector\")\n",
    "ax.w_yaxis.set_ticklabels([])\n",
    "ax.set_zlabel(\"3rd eigenvector\")\n",
    "ax.w_zaxis.set_ticklabels([])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploring the Digits Dataset\n",
    "\n",
    "_Note that much of the above exploration is not relevant or useful to the Digits dataset._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>16</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>15</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>11</td>\n",
       "      <td>16</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>15</td>\n",
       "      <td>13</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>13</td>\n",
       "      <td>13</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>16</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 65 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2   3   4   5  6  7  8  9  ...    55  56  57  58  59  60  61  62  63  \\\n",
       "0  0  0  5  13   9   1  0  0  0  0  ...     0   0   0   6  13  10   0   0   0   \n",
       "1  0  0  0  12  13   5  0  0  0  0  ...     0   0   0   0  11  16  10   0   0   \n",
       "2  0  0  0   4  15  12  0  0  0  0  ...     0   0   0   0   3  11  16   9   0   \n",
       "3  0  0  7  15  13   1  0  0  0  8  ...     0   0   0   7  13  13   9   0   0   \n",
       "4  0  0  0   1  11   0  0  0  0  0  ...     0   0   0   0   2  16   4   0   0   \n",
       "\n",
       "   class  \n",
       "0      0  \n",
       "1      1  \n",
       "2      2  \n",
       "3      3  \n",
       "4      4  \n",
       "\n",
       "[5 rows x 65 columns]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load digits dataset into a dataframe for exploration\n",
    "digits_df = pd.DataFrame(digits.data)\n",
    "digits_df['class'] = digits.target\n",
    "\n",
    "# Output head of iris dataframe for instance inspection\n",
    "digits_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAL8AAADDCAYAAADTCsC8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxXL4rVgOvxXL4bdiOfxWrP8CEMz+8G2LElYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2a697dae10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the first digit\n",
    "plt.figure(1, figsize=(3, 3))\n",
    "plt.imshow(digits.images[-1], cmap=plt.cm.gray_r, interpolation='nearest')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preparing the Data\n",
    "\n",
    "With some preliminary understanding of the dataset, we can move to preparing the data for analysis.\n",
    "\n",
    "We must prepare the datasets we will use for testing (fitting) the algorithms. Since we already have the Iris dataset loaded, we will go on to setting our predictor and target appropriately, creating testing and training sets to use repeatedly moving forward."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preparing the Iris Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/matt/bin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:15: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/home/matt/bin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:16: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/home/matt/bin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:17: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/home/matt/bin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:18: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    }
   ],
   "source": [
    "# X and y are the predictor and target, respectively\n",
    "X = iris.data\n",
    "y = iris.target\n",
    "\n",
    "# Number of samples in the iris dataset\n",
    "n_sample = len(X)\n",
    "\n",
    "# Split training/testing sets\n",
    "np.random.seed(0)\n",
    "order = np.random.permutation(n_sample)\n",
    "\n",
    "X = X[order]\n",
    "y = y[order].astype(np.float)\n",
    "\n",
    "X_train = X[:.9 * n_sample]\n",
    "y_train = y[:.9 * n_sample]\n",
    "X_test = X[.9 * n_sample:]\n",
    "y_test = y[.9 * n_sample:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preparing the Digits Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/matt/bin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:15: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/home/matt/bin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:16: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/home/matt/bin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:17: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/home/matt/bin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:18: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    }
   ],
   "source": [
    "# X_dig and y_dig are the predictor and target, respectively\n",
    "X_dig = digits.data\n",
    "y_dig = digits.target\n",
    "\n",
    "# Number of samples in the digits dataset\n",
    "n_sample_dig = len(X_dig)\n",
    "\n",
    "# Split training/testing sets\n",
    "np.random.seed(0)\n",
    "order = np.random.permutation(n_sample_dig)\n",
    "\n",
    "X_dig = X_dig[order]\n",
    "y_dig = y_dig[order].astype(np.float)\n",
    "\n",
    "X_dig_train = X_dig[:.9 * n_sample_dig]\n",
    "y_dig_train = y_dig[:.9 * n_sample_dig]\n",
    "X_dig_test = X_dig[.9 * n_sample_dig:]\n",
    "y_dig_test = y_dig[.9 * n_sample_dig:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some Useful Functions\n",
    "\n",
    "What follows are auxiliary functions used throughout the tutorial:\n",
    "\n",
    "* Function `conf_matrix()` is used to build, beautify, and return a [confusion matrix](https://en.wikipedia.org/wiki/Confusion_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import confusion matrix functionality\n",
    "from sklearn.metrics import confusion_matrix as sk_confusion_matrix\n",
    "\n",
    "# Create and format a confusion matrix\n",
    "def conf_matrix(y_test, y_predict):\n",
    "\n",
    "    # Create the raw confusion matrix\n",
    "    conf = sk_confusion_matrix(y_test, y_predict)\n",
    "\n",
    "    # Format the confusion matrix nicely\n",
    "    conf = pd.DataFrame(data=conf)\n",
    "    conf.columns.name = 'Predicted label'\n",
    "    conf.index.name = 'Actual label'\n",
    "\n",
    "    # Return the confusion matrix\n",
    "    return conf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression\n",
    "\n",
    "The first classification algorithm we will look at is [Logistic Regression](https://en.wikipedia.org/wiki/Logistic_regression)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Iris Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97037037037037033"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import logistic regression library\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "# Create the logistic regression model object\n",
    "logistic = LogisticRegression()\n",
    "\n",
    "# Train the model\n",
    "logistic.fit(X_train, y_train)\n",
    "\n",
    "# Check the score\n",
    "logistic.score(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic Model Coefficient:  [[ 0.4058485   1.42729388 -2.20620154 -1.01595183]\n",
      " [ 0.38233758 -1.49909611  0.53402104 -1.26826587]\n",
      " [-1.64410594 -1.43709915  2.35022066  2.50254717]]\n",
      "Logistic Model Intercept:  [ 0.26102942  0.97789476 -1.15656835]\n"
     ]
    }
   ],
   "source": [
    "# Output the equation coefficient and intercept\n",
    "print 'Logistic Model Coefficient: ', logistic.coef_\n",
    "print 'Logistic Model Intercept: ', logistic.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  2.,  0.,  1.,  1.,  2.,  1.,  0.,  0.,  0.,  2.,  1.,\n",
       "        2.,  0.])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the class of test set\n",
    "y_predict = logistic.predict(X_test)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  2.,  0.,  1.,  1.,  1.,  1.,  0.,  0.,  0.,  2.,  1.,\n",
       "        2.,  0.])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The *actual* class of test set\n",
    "y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted label</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual label</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted label  0  1  2\n",
       "Actual label            \n",
       "0                5  0  0\n",
       "1                0  5  1\n",
       "2                0  0  4"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the confusion matrix\n",
    "conf = conf_matrix(y_test, y_predict)\n",
    "\n",
    "# Output the confusion matrix\n",
    "conf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic Model Error Rate: 0.07\n"
     ]
    }
   ],
   "source": [
    "# When we were wrong, how wrong were we?\n",
    "# Error rate is the mean of how wrong our incorrect predictions were\n",
    "err_rate = (y_predict != y_test).mean()\n",
    "print('Logistic Model Error Rate: %.2f' % err_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Digits Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99443413729128016"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the logistic regression model object\n",
    "logistic_dig = LogisticRegression()\n",
    "\n",
    "# Train the model\n",
    "logistic_dig.fit(X_dig_train, y_dig_train)\n",
    "\n",
    "# Check the score\n",
    "logistic_dig.score(X_dig_train, y_dig_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic Model Coefficient:  [[  0.00000000e+00  -3.21915085e-02  -1.64057182e-02   5.32675842e-02\n",
      "   -8.23640118e-02  -3.54845620e-01  -2.82424884e-01  -3.37622892e-02\n",
      "   -1.42336507e-05  -7.99843831e-02  -8.59344272e-03   1.76114969e-01\n",
      "    1.79833885e-01   2.85924319e-01  -1.53284978e-02  -3.68534690e-02\n",
      "   -4.52253204e-03   7.26817826e-02   2.16286250e-01  -3.06707417e-02\n",
      "   -4.36300803e-01   3.23477586e-01  -1.11681407e-02  -1.41645538e-02\n",
      "   -2.25892134e-03   2.64241699e-02  -6.21057658e-02  -1.59788799e-01\n",
      "   -6.39744190e-01   1.00424432e-03   4.38405813e-02  -1.95988778e-04\n",
      "    0.00000000e+00   2.07861466e-01   1.45096264e-01  -1.45344017e-01\n",
      "   -6.10838656e-01  -3.11363816e-02  -5.50335833e-02   0.00000000e+00\n",
      "   -1.23724908e-03  -5.03737508e-02   2.29284678e-01  -3.08967312e-01\n",
      "   -2.54463657e-01   2.94773955e-03   1.16029387e-01  -8.54728057e-05\n",
      "   -1.51057988e-03  -1.25189478e-01   1.74301001e-02  -8.76335724e-02\n",
      "    4.35926131e-02  -3.61559701e-02  -2.37121946e-01  -7.78902471e-02\n",
      "   -3.96765798e-06  -4.70984640e-02  -2.64415233e-01   1.02870273e-01\n",
      "   -2.97817495e-01  -9.23842294e-02  -1.67792873e-01  -7.28837880e-02]\n",
      " [  0.00000000e+00   1.13976543e-01   4.91119844e-01   1.02193619e-01\n",
      "   -6.40667311e-01   4.75845047e-01  -3.49033981e-01  -2.76039317e-01\n",
      "   -4.09418954e-05  -1.33765015e+00  -5.26454955e-01  -3.62342676e-01\n",
      "    2.77411582e-02   2.30252896e-01  -4.12705683e-01  -2.80297672e-02\n",
      "    2.28530831e-01   7.75480415e-01   3.78740717e-02   7.26542739e-01\n",
      "    2.86339460e-01  -3.81071791e-01   4.27515665e-01  -1.39884041e-01\n",
      "    1.14289971e-01  -3.44749609e-01   1.94741214e-02   4.43092166e-02\n",
      "    1.67751351e-01   1.14775051e-01  -4.82899868e-01  -3.79152411e-06\n",
      "    0.00000000e+00   4.89890433e-02  -2.06918845e-02  -5.32793038e-02\n",
      "    1.27805752e-01   3.07547589e-03  -3.26610313e-01   0.00000000e+00\n",
      "   -1.27385634e-05  -9.61941946e-01   7.64455112e-02  -5.31388967e-02\n",
      "   -9.35673972e-02  -4.15383844e-01  -2.24636337e-01  -1.94694178e-01\n",
      "   -2.53964821e-02   2.38839873e-01  -1.91998630e-01   2.11827181e-01\n",
      "   -3.12962071e-03   4.53943086e-02  -4.38997582e-01   6.83241636e-01\n",
      "   -8.46384204e-03  -1.06142211e+00  -4.79594588e-01  -5.66032268e-02\n",
      "    9.22071794e-02   1.39209869e-01  -1.67660212e-01   9.38947966e-02]\n",
      " [  0.00000000e+00   4.92117554e-02  -6.03183988e-02   1.20813024e-02\n",
      "   -3.99864728e-02  -2.49100191e-01  -1.41019367e-01  -1.62604623e-02\n",
      "   -3.81485938e-04   1.35619199e-01   2.24615290e-01  -1.67016451e-01\n",
      "    2.25666636e-01  -3.81005487e-02  -2.73201150e-02  -3.99713942e-03\n",
      "   -9.19441742e-05  -1.10508019e-01   8.38537426e-02  -2.16977728e-01\n",
      "    1.98753055e-01   1.18901672e-02   8.84220715e-02  -2.33219471e-04\n",
      "   -2.66164210e-05  -2.82830343e-01  -6.12001125e-01  -5.38443673e-01\n",
      "   -3.36614773e-01   1.82038408e-01  -1.10101589e-01  -9.71896724e-06\n",
      "    0.00000000e+00  -3.02672452e-01  -5.40675700e-01  -1.46657722e-01\n",
      "   -2.32062662e-01  -3.43790542e-01  -5.47972669e-01   0.00000000e+00\n",
      "   -5.99738541e-05   7.51580194e-02   1.10531602e-01   4.51498653e-01\n",
      "   -4.51758411e-01  -4.58812258e-01  -4.18649460e-01   1.16560037e-02\n",
      "    3.69892231e-03   2.57342650e-01  -2.89271722e-02   4.30659579e-01\n",
      "    2.63890506e-01   2.65315220e-01   2.10885317e-01   1.22751116e-02\n",
      "    1.24486172e-03   1.05218424e-01   7.82855522e-03  -4.36562120e-02\n",
      "   -4.61813580e-02   2.22502654e-01   3.67075200e-01   1.91112814e-02]\n",
      " [  0.00000000e+00   1.00155545e-01  -8.39543283e-01   1.60447685e-01\n",
      "    5.04845289e-01  -1.26924513e-01  -1.31085629e-01   1.29644415e-01\n",
      "   -1.10992739e-02  -3.56722290e-02   3.42357851e-01   4.96431042e-02\n",
      "    2.68346231e-02   6.49243692e-01   6.98296558e-01  -3.69790715e-01\n",
      "   -1.30638263e-04   1.49377550e-01  -7.39115168e-01  -3.50648547e-01\n",
      "    2.02124163e-01  -4.35215274e-01   3.61406375e-01  -7.13738816e-04\n",
      "   -1.66404168e-07  -3.91058752e-01  -5.85987300e-01   1.61569493e-01\n",
      "    8.07445662e-02  -7.19595524e-01  -1.98690341e+00  -6.44584753e-07\n",
      "    0.00000000e+00  -3.27051047e-01  -3.23431445e-01  -1.58618741e-01\n",
      "   -1.46186521e-01   4.22405991e-02   1.84696798e-01   0.00000000e+00\n",
      "   -1.97220476e-06  -4.98957886e-02  -2.34314880e-01  -1.06931419e+00\n",
      "    3.75015583e-01   2.15129172e-01   3.82146352e-01  -9.71209553e-04\n",
      "   -2.54764834e-06  -1.32475459e-01  -5.58340390e-02  -2.51356538e-01\n",
      "   -4.43551563e-02   3.82333222e-01   6.99772106e-01  -8.56535215e-01\n",
      "   -3.45998840e-07   4.86033707e-01   3.45717285e-01  -4.52758266e-01\n",
      "    1.18074952e-01  -3.03453161e-01   1.78393101e-02  -1.10929418e+00]\n",
      " [  0.00000000e+00  -2.04116415e-02  -2.98279881e-01  -5.56785931e-01\n",
      "   -2.43071244e-01  -3.92644820e-01  -4.63926799e-01   1.16047222e-01\n",
      "   -3.18073782e-05   2.07364717e-02  -2.70772810e-02  -2.97876811e-01\n",
      "   -4.53615073e-01  -2.81735974e-01  -2.99150133e-01   1.38647088e-01\n",
      "   -6.41692851e-04  -1.93025246e-02   3.91605346e-01   6.06994701e-02\n",
      "    4.88912230e-02   2.54265694e-01   2.01971482e-02   8.72347844e-02\n",
      "   -3.18721584e-04  -9.80090680e-02   3.60582347e-01   1.04792147e-01\n",
      "   -2.09546521e-01  -4.23344764e-03   5.26815972e-01   3.00710710e-03\n",
      "    0.00000000e+00   1.71019642e-01   2.07723943e-02   9.82892617e-02\n",
      "    3.29015657e-01   9.89238202e-02   4.01917649e-01   0.00000000e+00\n",
      "    1.22640431e-03   5.86317617e-01  -1.04109419e-01   3.45529873e-01\n",
      "    1.11226112e-01   1.65817725e-01   3.78889534e-02  -1.29663431e-03\n",
      "    2.19561257e-03   3.59905863e-01  -1.52680291e-01   7.40743358e-02\n",
      "    1.22842335e-01  -3.79148091e-01  -5.00722945e-01  -4.56813374e-03\n",
      "   -3.64926491e-05  -1.03225304e-01  -2.05643110e-01  -3.62565368e-01\n",
      "   -2.96715805e-01  -1.99620807e-01  -1.05216484e-01  -2.55464225e-03]\n",
      " [  0.00000000e+00   8.91427353e-03   7.33303509e-01  -4.45255526e-01\n",
      "   -2.48133037e-02   3.68093900e-01   6.46177399e-01  -1.57326469e-01\n",
      "    3.78389212e-03  -4.65979768e-03   7.95749567e-02   9.01543984e-03\n",
      "    7.42419085e-02  -1.54926314e-01  -3.74883720e-01  -8.62198624e-02\n",
      "   -2.77073619e-02  -2.78468439e-01   4.19841350e-01   2.19427759e-01\n",
      "   -6.06523355e-01  -6.83367613e-01  -1.05607170e+00  -9.93409065e-03\n",
      "   -1.38513129e-02   4.77609116e-02   3.92739563e-01  -1.57239022e-01\n",
      "    3.28501945e-01  -1.30520300e-01  -1.17674110e+00  -6.11930571e-06\n",
      "    0.00000000e+00  -2.99350690e-01   1.16748265e-01  -2.64011335e-01\n",
      "   -3.76107151e-01  -1.78058583e-01   4.33207061e-01   0.00000000e+00\n",
      "   -1.19744396e-06  -3.09633701e-01  -3.68730744e-01  -3.43328630e-01\n",
      "   -2.12288620e-01   1.79723361e-01  -3.02046703e-02  -8.73709634e-04\n",
      "    9.35231410e-06   8.26530838e-02  -3.68848926e-01   1.49814498e-01\n",
      "   -6.73453761e-02  -1.24565419e-01  -6.18316149e-01  -1.75216924e-02\n",
      "    1.36886389e-06  -1.41447407e-01   2.29129712e-01   2.86192359e-01\n",
      "    9.61801909e-03  -1.99700958e-02  -5.66433737e-01  -9.41372578e-02]\n",
      " [  0.00000000e+00  -3.73477442e-02  -2.50790708e-01  -1.43158183e-01\n",
      "   -2.15724969e-01  -3.21636609e-01  -2.00120979e-01  -2.64216276e-04\n",
      "   -3.66135747e-05  -3.53037251e-01  -6.50944913e-02  -2.46450870e-01\n",
      "   -4.51405660e-01   1.46833179e-01   1.37999234e-01  -4.12114011e-04\n",
      "   -1.55962196e-02  -1.15471114e-01   8.53920885e-02   1.87737028e-01\n",
      "   -5.62469767e-01  -9.06411423e-01  -3.21082361e-01  -3.57797944e-04\n",
      "   -7.79436320e-03   4.19602348e-01  -2.25886784e-02   2.88238267e-01\n",
      "   -7.67403681e-02  -8.25855389e-02  -6.67922921e-01  -2.87170133e-05\n",
      "    0.00000000e+00   2.10041849e-01   1.47294889e-01   1.97781299e-01\n",
      "   -7.88962446e-02   1.52825041e-02  -5.21838423e-02   0.00000000e+00\n",
      "   -1.02455483e-03  -8.01447076e-01   6.74687476e-01  -1.61213204e-01\n",
      "    2.19036915e-01  -1.85589293e-01   5.01773335e-01   7.37952718e-02\n",
      "   -2.86386711e-04  -3.15282885e-01   3.42141916e-01   2.54043906e-01\n",
      "   -3.23751138e-01   3.56295453e-01   2.67037146e-02  -5.85047800e-01\n",
      "   -1.11103010e-06  -2.41668893e-02  -3.40462333e-01  -3.05645551e-01\n",
      "   -1.61576124e-01   1.15979478e-01  -1.96629207e-01  -2.32675744e-01]\n",
      " [  0.00000000e+00  -2.10658207e-01   2.43573956e-01   2.81688327e-01\n",
      "   -2.12679911e-01   4.28758684e-01   3.39224812e-01   1.90694153e-01\n",
      "   -2.46210414e-05   7.91550341e-02   1.41378232e-01  -1.28432281e-01\n",
      "    8.52317730e-01  -1.56272288e-01  -1.89330808e-01   2.71105475e-01\n",
      "   -1.49962368e-05  -2.41044500e-01  -3.90369873e-01  -4.23223044e-01\n",
      "   -2.75164454e-01   3.57124071e-01   1.32827540e-01   3.32815278e-02\n",
      "   -3.50869624e-06  -5.43276349e-01  -4.41173441e-02  -4.43752961e-01\n",
      "   -6.47752053e-02   8.60717395e-03   2.11838428e-01  -5.05433398e-03\n",
      "    0.00000000e+00   5.06333180e-01  -1.59104529e-01   9.30092596e-02\n",
      "    8.87154514e-02   5.75028562e-02   3.20257459e-01   0.00000000e+00\n",
      "   -1.89197314e-04  -4.17225899e-01   6.80305315e-02  -2.34968053e-02\n",
      "    1.89120615e-01   2.65143568e-01  -2.27029729e-02  -7.48171038e-05\n",
      "   -5.73262758e-05  -2.17749491e-01   1.37982632e-01   1.25435446e-01\n",
      "   -6.52443548e-01  -1.08390164e+00  -2.36014094e-01  -1.00057700e-03\n",
      "   -1.40858171e-05  -4.18994757e-01  -3.01276371e-01  -3.12427048e-01\n",
      "   -7.17950834e-02  -7.83793444e-01  -2.48229121e-01  -1.51528883e-02]\n",
      " [  0.00000000e+00  -1.79358242e-01   1.99273168e-01  -1.72664409e-01\n",
      "   -3.42423637e-02   2.48612798e-02  -5.86852906e-01  -6.85671996e-02\n",
      "    1.25090398e+00  -2.66766215e-02   1.40768698e-01  -8.18261204e-03\n",
      "   -1.55250600e-01   1.17397352e-01   1.58709278e-01  -2.00902708e-01\n",
      "   -3.35910147e-01   1.33460076e-01   1.60680856e-01   7.14341350e-02\n",
      "   -3.83670412e-03   1.22708825e-01   1.66900412e-01  -1.20280126e-01\n",
      "   -4.79022512e-01  -1.28007769e-01  -5.16770814e-02   1.59920883e-01\n",
      "   -1.03424127e-01   7.59204318e-03  -1.60561426e-01  -2.51205644e-03\n",
      "    0.00000000e+00  -4.06947810e-01  -9.27404141e-02   2.67172436e-01\n",
      "    6.77209253e-03  -7.91194536e-02  -9.34343306e-01   0.00000000e+00\n",
      "   -5.95261747e-04   1.79176787e-01   1.21652108e-01   2.45291047e-02\n",
      "    8.45451058e-03   5.43475699e-02   9.99523572e-03  -1.36127444e-01\n",
      "   -4.61680704e-02  -6.08488874e-02   1.71687396e-01  -2.31701248e-01\n",
      "   -1.74763527e-01   7.38181011e-02   1.90457099e-02  -3.97526114e-02\n",
      "   -1.53497713e-02  -2.45877190e-02  -5.07807339e-01  -4.14743434e-02\n",
      "    5.38597500e-02  -1.95782098e-01  -1.83180645e-01  -9.91218264e-02]\n",
      " [  0.00000000e+00  -9.70298329e-01   1.56337849e-01   1.33979388e-01\n",
      "    1.15101109e-01  -2.93697392e-01  -1.83636211e-01  -1.88115658e-01\n",
      "   -4.49826163e-03   1.16287278e-01  -1.20848885e-03   2.46607620e-01\n",
      "   -1.16782118e-01  -1.42521938e-01   4.04016579e-01  -4.55880937e-01\n",
      "   -9.56097265e-02   2.35764081e-01   3.34948682e-01   1.36063517e-01\n",
      "    1.63228631e-01   6.96317334e-01  -1.39508209e-01  -4.57561695e-01\n",
      "   -4.63952752e-02  -2.60352456e-01   1.86800907e-01   3.49837549e-01\n",
      "   -2.57459371e-01   2.45224777e-01  -3.13224815e-02  -4.22946065e-02\n",
      "    0.00000000e+00  -6.31193186e-01  -3.22368745e-01   5.70493011e-01\n",
      "   -2.53656787e-01  -3.26841683e-02   1.81079075e-01   0.00000000e+00\n",
      "   -1.70901712e-06  -1.36075012e-01  -6.91064084e-01  -1.38237446e+00\n",
      "   -5.26692824e-01  -3.19400630e-01  -5.24283130e-01   3.08782392e-05\n",
      "   -2.04823523e-06   1.68940504e-02  -2.87930767e-02  -2.03527776e-02\n",
      "   -3.20545631e-01  -2.93471502e-01  -1.17186702e-01   7.95796644e-01\n",
      "   -2.25939668e-07  -6.20398953e-01  -2.18571042e-01  -7.22444712e-02\n",
      "   -2.19294974e-02  -9.61207979e-02  -6.85181613e-02  -3.77440516e-01]]\n",
      "Logistic Model Intercept:  [-0.01943198 -2.24414524 -0.0359581  -0.33811924  0.01443993 -0.10700609\n",
      " -0.07197064 -0.02320032 -2.6808876  -1.08720675]\n"
     ]
    }
   ],
   "source": [
    "# Output the equation coefficient and intercept\n",
    "print 'Logistic Model Coefficient: ', logistic_dig.coef_\n",
    "print 'Logistic Model Intercept: ', logistic_dig.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.,  6.,  1.,  7.,  4.,  1.,  4.,  7.,  0.,  1.,  5.,  6.,  2.,\n",
       "        7.,  8.,  4.,  8.,  0.,  9.,  0.,  5.,  2.,  2.,  4.,  1.,  8.,\n",
       "        8.,  7.,  2.,  9.,  7.,  0.,  0.,  6.,  0.,  5.,  0.,  5.,  1.,\n",
       "        0.,  1.,  6.,  6.,  0.,  3.,  4.,  0.,  3.,  5.,  6.,  9.,  8.,\n",
       "        4.,  8.,  5.,  2.,  7.,  5.,  5.,  1.,  1.,  8.,  9.,  0.,  3.,\n",
       "        4.,  9.,  2.,  9.,  7.,  1.,  7.,  5.,  4.,  9.,  5.,  7.,  7.,\n",
       "        7.,  0.,  1.,  9.,  1.,  9.,  7.,  1.,  3.,  9.,  4.,  9.,  2.,\n",
       "        5.,  3.,  5.,  6.,  2.,  3.,  0.,  7.,  5.,  2.,  3.,  2.,  6.,\n",
       "        1.,  7.,  0.,  2.,  9.,  4.,  2.,  0.,  7.,  4.,  4.,  9.,  0.,\n",
       "        4.,  9.,  6.,  8.,  2.,  6.,  4.,  4.,  9.,  1.,  2.,  4.,  7.,\n",
       "        8.,  1.,  2.,  2.,  5.,  9.,  5.,  4.,  3.,  1.,  4.,  7.,  1.,\n",
       "        5.,  3.,  8.,  6.,  5.,  5.,  2.,  1.,  0.,  9.,  1.,  6.,  9.,\n",
       "        3.,  7.,  1.,  5.,  6.,  3.,  6.,  5.,  2.,  9.,  6.,  3.,  4.,\n",
       "        1.,  8.,  4.,  8.,  4.,  5.,  3.,  3.,  7.,  7.,  8.])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the class of test set\n",
    "y_dig_predict = logistic_dig.predict(X_dig_test)\n",
    "y_dig_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.,  6.,  1.,  7.,  4.,  1.,  4.,  7.,  0.,  1.,  5.,  6.,  2.,\n",
       "        7.,  8.,  4.,  9.,  0.,  9.,  0.,  5.,  2.,  2.,  4.,  1.,  8.,\n",
       "        8.,  7.,  2.,  9.,  7.,  0.,  0.,  6.,  0.,  5.,  0.,  5.,  1.,\n",
       "        0.,  8.,  6.,  6.,  0.,  3.,  4.,  0.,  3.,  5.,  6.,  9.,  8.,\n",
       "        4.,  8.,  5.,  2.,  7.,  5.,  5.,  1.,  1.,  8.,  9.,  0.,  3.,\n",
       "        4.,  9.,  2.,  9.,  3.,  1.,  7.,  5.,  4.,  9.,  5.,  7.,  7.,\n",
       "        7.,  0.,  1.,  9.,  1.,  9.,  7.,  1.,  3.,  9.,  4.,  9.,  2.,\n",
       "        5.,  3.,  5.,  6.,  2.,  3.,  0.,  7.,  3.,  2.,  5.,  2.,  6.,\n",
       "        1.,  7.,  0.,  2.,  9.,  4.,  2.,  0.,  7.,  4.,  4.,  9.,  0.,\n",
       "        4.,  9.,  6.,  8.,  2.,  6.,  4.,  4.,  9.,  1.,  2.,  4.,  7.,\n",
       "        8.,  8.,  2.,  2.,  5.,  9.,  5.,  4.,  3.,  1.,  4.,  7.,  1.,\n",
       "        5.,  3.,  8.,  6.,  5.,  5.,  2.,  1.,  0.,  9.,  1.,  6.,  9.,\n",
       "        3.,  7.,  4.,  5.,  6.,  3.,  6.,  5.,  2.,  7.,  6.,  3.,  4.,\n",
       "        1.,  1.,  4.,  8.,  4.,  5.,  3.,  3.,  7.,  7.,  8.])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The *actual* class of test set\n",
    "y_dig_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted label</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual label</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>13</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>21</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted label   0   1   2   3   4   5   6   7   8   9\n",
       "Actual label                                           \n",
       "0                17   0   0   0   0   0   0   0   0   0\n",
       "1                 0  18   0   0   0   0   0   0   1   0\n",
       "2                 0   0  18   0   0   0   0   0   0   0\n",
       "3                 0   0   0  13   0   1   0   1   0   0\n",
       "4                 0   1   0   0  21   0   0   0   0   0\n",
       "5                 0   0   0   1   0  20   0   0   0   0\n",
       "6                 0   0   0   0   0   0  15   0   0   0\n",
       "7                 0   0   0   0   0   0   0  19   0   1\n",
       "8                 0   2   0   0   0   0   0   0  12   0\n",
       "9                 0   0   0   0   0   0   0   0   1  18"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the confusion matrix\n",
    "conf_dig = conf_matrix(y_dig_test, y_dig_predict)\n",
    "\n",
    "# Output the confusion matrix\n",
    "conf_dig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic Model Error Rate: 0.05\n"
     ]
    }
   ],
   "source": [
    "# When we were wrong, how wrong were we?\n",
    "# Error rate is the mean of how wrong our incorrect predictions were\n",
    "err_rate_dig_lr = (y_dig_predict != y_dig_test).mean()\n",
    "print('Logistic Model Error Rate: %.2f' % err_rate_dig_lr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decision Tree\n",
    "\n",
    "The next classifier we will look at is the [Decision Tree](https://en.wikipedia.org/wiki/Decision_tree)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Iris Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import logistic regression library\n",
    "from sklearn import tree\n",
    "\n",
    "# Create the logistic regression model object using information gain\n",
    "decision = tree.DecisionTreeClassifier(criterion='entropy')\n",
    "\n",
    "# Train the model\n",
    "decision.fit(X_train, y_train)\n",
    "\n",
    "# Check the score\n",
    "decision.score(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  2.,  0.,  1.,  1.,  2.,  1.,  0.,  0.,  0.,  2.,  1.,\n",
       "        2.,  0.])"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the class of test set\n",
    "y_predict = decision.predict(X_test)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  2.,  0.,  1.,  1.,  1.,  1.,  0.,  0.,  0.,  2.,  1.,\n",
       "        2.,  0.])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The *actual* class of test set\n",
    "y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted label</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual label</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted label  0  1  2\n",
       "Actual label            \n",
       "0                5  0  0\n",
       "1                0  5  1\n",
       "2                0  0  4"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the confusion matrix\n",
    "conf = conf_matrix(y_test, y_predict)\n",
    "\n",
    "# Output the confusion matrix\n",
    "conf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decision Tree Model Error Rate: 0.07\n"
     ]
    }
   ],
   "source": [
    "# When we were wrong, how wrong were we?\n",
    "# Error rate is the mean of how wrong our incorrect predictions were\n",
    "err_rate = (y_predict != y_test).mean()\n",
    "print('Decision Tree Model Error Rate: %.2f' % err_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Digits Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the logistic regression model object using information gain\n",
    "decision_dig = tree.DecisionTreeClassifier(criterion='entropy')\n",
    "\n",
    "# Train the model\n",
    "decision_dig.fit(X_dig_train, y_dig_train)\n",
    "\n",
    "# Check the score\n",
    "decision_dig.score(X_dig_train, y_dig_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.,  6.,  1.,  7.,  4.,  1.,  4.,  7.,  0.,  1.,  5.,  6.,  2.,\n",
       "        7.,  8.,  4.,  9.,  0.,  9.,  0.,  5.,  2.,  2.,  4.,  1.,  4.,\n",
       "        8.,  7.,  2.,  9.,  7.,  0.,  0.,  6.,  0.,  5.,  0.,  5.,  1.,\n",
       "        0.,  8.,  6.,  6.,  0.,  3.,  4.,  0.,  3.,  5.,  6.,  9.,  8.,\n",
       "        4.,  8.,  5.,  2.,  7.,  5.,  5.,  1.,  1.,  8.,  9.,  0.,  3.,\n",
       "        6.,  9.,  2.,  9.,  7.,  1.,  7.,  5.,  4.,  1.,  5.,  0.,  7.,\n",
       "        7.,  0.,  1.,  9.,  1.,  2.,  7.,  1.,  2.,  9.,  4.,  9.,  2.,\n",
       "        9.,  3.,  5.,  6.,  2.,  3.,  0.,  4.,  5.,  2.,  5.,  2.,  6.,\n",
       "        1.,  7.,  0.,  2.,  9.,  4.,  2.,  0.,  7.,  4.,  4.,  9.,  0.,\n",
       "        4.,  9.,  6.,  8.,  2.,  6.,  4.,  8.,  9.,  1.,  1.,  4.,  7.,\n",
       "        8.,  8.,  2.,  2.,  5.,  9.,  5.,  4.,  1.,  1.,  4.,  7.,  1.,\n",
       "        5.,  3.,  3.,  6.,  8.,  5.,  8.,  1.,  0.,  9.,  1.,  6.,  9.,\n",
       "        3.,  7.,  7.,  5.,  6.,  3.,  6.,  5.,  2.,  7.,  6.,  1.,  4.,\n",
       "        8.,  1.,  0.,  8.,  4.,  5.,  3.,  3.,  7.,  7.,  8.])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the class of test set\n",
    "y_dig_predict = decision_dig.predict(X_dig_test)\n",
    "y_dig_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.,  6.,  1.,  7.,  4.,  1.,  4.,  7.,  0.,  1.,  5.,  6.,  2.,\n",
       "        7.,  8.,  4.,  9.,  0.,  9.,  0.,  5.,  2.,  2.,  4.,  1.,  8.,\n",
       "        8.,  7.,  2.,  9.,  7.,  0.,  0.,  6.,  0.,  5.,  0.,  5.,  1.,\n",
       "        0.,  8.,  6.,  6.,  0.,  3.,  4.,  0.,  3.,  5.,  6.,  9.,  8.,\n",
       "        4.,  8.,  5.,  2.,  7.,  5.,  5.,  1.,  1.,  8.,  9.,  0.,  3.,\n",
       "        4.,  9.,  2.,  9.,  3.,  1.,  7.,  5.,  4.,  9.,  5.,  7.,  7.,\n",
       "        7.,  0.,  1.,  9.,  1.,  9.,  7.,  1.,  3.,  9.,  4.,  9.,  2.,\n",
       "        5.,  3.,  5.,  6.,  2.,  3.,  0.,  7.,  3.,  2.,  5.,  2.,  6.,\n",
       "        1.,  7.,  0.,  2.,  9.,  4.,  2.,  0.,  7.,  4.,  4.,  9.,  0.,\n",
       "        4.,  9.,  6.,  8.,  2.,  6.,  4.,  4.,  9.,  1.,  2.,  4.,  7.,\n",
       "        8.,  8.,  2.,  2.,  5.,  9.,  5.,  4.,  3.,  1.,  4.,  7.,  1.,\n",
       "        5.,  3.,  8.,  6.,  5.,  5.,  2.,  1.,  0.,  9.,  1.,  6.,  9.,\n",
       "        3.,  7.,  4.,  5.,  6.,  3.,  6.,  5.,  2.,  7.,  6.,  3.,  4.,\n",
       "        1.,  1.,  4.,  8.,  4.,  5.,  3.,  3.,  7.,  7.,  8.])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The *actual* class of test set\n",
    "y_dig_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted label</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual label</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted label   0   1   2   3   4   5   6   7   8   9\n",
       "Actual label                                           \n",
       "0                17   0   0   0   0   0   0   0   0   0\n",
       "1                 0  18   0   0   0   0   0   0   1   0\n",
       "2                 0   1  16   0   0   0   0   0   1   0\n",
       "3                 0   2   1  10   0   1   0   1   0   0\n",
       "4                 1   0   0   0  18   0   1   1   1   0\n",
       "5                 0   0   0   0   0  19   0   0   1   1\n",
       "6                 0   0   0   0   0   0  15   0   0   0\n",
       "7                 1   0   0   0   1   0   0  18   0   0\n",
       "8                 0   0   0   1   1   0   0   0  12   0\n",
       "9                 0   1   1   0   0   0   0   0   0  17"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the confusion matrix\n",
    "conf_dig = conf_matrix(y_dig_test, y_dig_predict)\n",
    "\n",
    "# Output the confusion matrix\n",
    "conf_dig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decision Tree Model Error Rate: 0.11\n"
     ]
    }
   ],
   "source": [
    "# When we were wrong, how wrong were we?\n",
    "# Error rate is the mean of how wrong our incorrect predictions were\n",
    "err_rate_dig_dt = (y_dig_predict != y_dig_test).mean()\n",
    "print('Decision Tree Model Error Rate: %.2f' % err_rate_dig_dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Support Vector Machine\n",
    "\n",
    "Using cross-validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVM Cross-validation Scores: [ 1.          0.93333333  1.          1.          0.86666667  1.\n",
      "  0.93333333  1.          1.          1.        ]\n"
     ]
    }
   ],
   "source": [
    "# Import SVM library\n",
    "from sklearn import svm\n",
    "\n",
    "# Impot cross-validation functionality\n",
    "from sklearn import cross_validation\n",
    "\n",
    "# Build the (linear) SVM model object\n",
    "clf = svm.SVC(kernel='linear', C=1)\n",
    "\n",
    "# Evaluate using 10-fold cross-validation\n",
    "scores = cross_validation.cross_val_score(clf, iris.data, iris.target, cv=10)\n",
    "\n",
    "# Display the individual CV scores\n",
    "print 'SVM Cross-validation Scores:', scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mvHn4YffBg9OOonQnnug+a1baURRH7bz2RZ+dRX+eJ9b15O5vEbqTpgHPAL9192Vmdr6Z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\nRCEiIrGUKEREJJYShYiIxPpfrhL96KCKgr4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2a64036410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot fold scores\n",
    "folds = range(1, 11)\n",
    "folds = np.array(folds)\n",
    "\n",
    "plt.xlabel('Fold')\n",
    "plt.ylabel('Score')\n",
    "plt.ylim([0.8,1.02])\n",
    "plt.xlim([1.0,10.0])\n",
    "\n",
    "plt.scatter(folds, scores, color='red')\n",
    "plt.plot(folds, scores, color='blue')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean SVM Cross-validation Score: 0.973333333333\n"
     ]
    }
   ],
   "source": [
    "# Mean CV evaluation score\n",
    "print 'Mean SVM Cross-validation Score:', scores.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Digits Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Iris Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVM Cross-validation Scores: [ 0.93513514  0.99453552  0.9281768   0.96111111  0.96089385  0.98882682\n",
      "  0.96648045  0.97752809  0.93220339  0.96590909]\n"
     ]
    }
   ],
   "source": [
    "# Build the (linear) SVM model object\n",
    "clf_dig = svm.SVC(kernel='linear', C=1)\n",
    "\n",
    "# Evaluate using 10-fold cross-validation\n",
    "scores_dig = cross_validation.cross_val_score(clf_dig, digits.data, digits.target, cv=10)\n",
    "\n",
    "# Display the individual CV scores\n",
    "print 'SVM Cross-validation Scores:', scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ytx5HppSVhZvJESNCkqiuO7cSRYwhQ8K0wx98UFijMs8/P4xt+uc/k44kPcuXh14l33wD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\nChERiaVEISIisZQoREQklhKFiIjE+n+VxkagiVO5SwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2a64066110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot fold scores\n",
    "folds_dig = range(1, 11)\n",
    "folds_dig = np.array(folds_dig)\n",
    "\n",
    "plt.xlabel('Fold')\n",
    "plt.ylabel('Score')\n",
    "plt.ylim([0.8,1.02])\n",
    "plt.xlim([1.0,10.0])\n",
    "\n",
    "plt.scatter(folds_dig, scores_dig, color='red')\n",
    "plt.plot(folds_dig, scores_dig, color='blue')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean SVM Cross-validation Score: 0.96108002489\n"
     ]
    }
   ],
   "source": [
    "# Mean CV evaluation score\n",
    "print 'Mean SVM Cross-validation Score:', scores_dig.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Naive Bayes\n",
    "\n",
    "Next we look at the [Naive Bayes](https://en.wikipedia.org/wiki/Naive_Bayes_classifier) classifier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Iris Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.96296296296296291"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import Naive Bayes library\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "\n",
    "# Create the Naive Bayes model object\n",
    "nb = GaussianNB()\n",
    "\n",
    "# Train the model\n",
    "nb.fit(X_train, y_train)\n",
    "\n",
    "# Check the score\n",
    "nb.score(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  2.,  0.,  1.,  1.,  2.,  1.,  0.,  0.,  0.,  2.,  1.,\n",
       "        2.,  0.])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the class of test set\n",
    "y_predict = nb.predict(X_test)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  2.,  0.,  1.,  1.,  1.,  1.,  0.,  0.,  0.,  2.,  1.,\n",
       "        2.,  0.])"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The *actual* class of test set\n",
    "y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted label</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual label</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted label  0  1  2\n",
       "Actual label            \n",
       "0                5  0  0\n",
       "1                0  5  1\n",
       "2                0  0  4"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the confusion matrix\n",
    "conf = conf_matrix(y_test, y_predict)\n",
    "\n",
    "# Output the confusion matrix\n",
    "conf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Naive Bayes Model Error Rate: 0.07\n"
     ]
    }
   ],
   "source": [
    "# When we were wrong, how wrong were we?\n",
    "# Error rate is the mean of how wrong our incorrect predictions were\n",
    "err_rate = (y_predict != y_test).mean()\n",
    "print('Naive Bayes Model Error Rate: %.2f' % err_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Digits Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.83240568954854666"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the Naive Bayes model object\n",
    "nb_dig = GaussianNB()\n",
    "\n",
    "# Train the model\n",
    "nb_dig.fit(X_dig_train, y_dig_train)\n",
    "\n",
    "# Check the score\n",
    "nb_dig.score(X_dig_train, y_dig_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.,  6.,  1.,  7.,  4.,  1.,  7.,  7.,  0.,  1.,  5.,  6.,  8.,\n",
       "        7.,  8.,  4.,  7.,  0.,  1.,  0.,  5.,  2.,  8.,  7.,  1.,  8.,\n",
       "        8.,  7.,  8.,  8.,  7.,  0.,  0.,  6.,  0.,  5.,  0.,  5.,  1.,\n",
       "        0.,  1.,  6.,  6.,  0.,  3.,  4.,  0.,  8.,  5.,  6.,  8.,  8.,\n",
       "        4.,  8.,  5.,  2.,  7.,  5.,  5.,  1.,  1.,  8.,  9.,  0.,  8.,\n",
       "        4.,  9.,  2.,  9.,  7.,  1.,  7.,  5.,  4.,  1.,  5.,  7.,  7.,\n",
       "        7.,  0.,  1.,  8.,  1.,  8.,  7.,  8.,  3.,  7.,  4.,  9.,  8.,\n",
       "        7.,  3.,  5.,  6.,  1.,  3.,  0.,  7.,  8.,  1.,  5.,  8.,  6.,\n",
       "        1.,  7.,  0.,  8.,  8.,  4.,  2.,  0.,  7.,  2.,  4.,  9.,  0.,\n",
       "        4.,  9.,  6.,  8.,  2.,  6.,  4.,  8.,  9.,  1.,  8.,  4.,  7.,\n",
       "        8.,  1.,  8.,  2.,  5.,  9.,  5.,  4.,  3.,  1.,  4.,  7.,  1.,\n",
       "        5.,  8.,  8.,  6.,  5.,  5.,  8.,  1.,  0.,  9.,  1.,  6.,  9.,\n",
       "        8.,  7.,  1.,  5.,  6.,  3.,  6.,  5.,  2.,  7.,  6.,  2.,  4.,\n",
       "        1.,  8.,  4.,  8.,  4.,  5.,  8.,  3.,  7.,  7.,  8.])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the class of test set\n",
    "y_dig_predict = nb_dig.predict(X_dig_test)\n",
    "y_dig_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.,  6.,  1.,  7.,  4.,  1.,  4.,  7.,  0.,  1.,  5.,  6.,  2.,\n",
       "        7.,  8.,  4.,  9.,  0.,  9.,  0.,  5.,  2.,  2.,  4.,  1.,  8.,\n",
       "        8.,  7.,  2.,  9.,  7.,  0.,  0.,  6.,  0.,  5.,  0.,  5.,  1.,\n",
       "        0.,  8.,  6.,  6.,  0.,  3.,  4.,  0.,  3.,  5.,  6.,  9.,  8.,\n",
       "        4.,  8.,  5.,  2.,  7.,  5.,  5.,  1.,  1.,  8.,  9.,  0.,  3.,\n",
       "        4.,  9.,  2.,  9.,  3.,  1.,  7.,  5.,  4.,  9.,  5.,  7.,  7.,\n",
       "        7.,  0.,  1.,  9.,  1.,  9.,  7.,  1.,  3.,  9.,  4.,  9.,  2.,\n",
       "        5.,  3.,  5.,  6.,  2.,  3.,  0.,  7.,  3.,  2.,  5.,  2.,  6.,\n",
       "        1.,  7.,  0.,  2.,  9.,  4.,  2.,  0.,  7.,  4.,  4.,  9.,  0.,\n",
       "        4.,  9.,  6.,  8.,  2.,  6.,  4.,  4.,  9.,  1.,  2.,  4.,  7.,\n",
       "        8.,  8.,  2.,  2.,  5.,  9.,  5.,  4.,  3.,  1.,  4.,  7.,  1.,\n",
       "        5.,  3.,  8.,  6.,  5.,  5.,  2.,  1.,  0.,  9.,  1.,  6.,  9.,\n",
       "        3.,  7.,  4.,  5.,  6.,  3.,  6.,  5.,  2.,  7.,  6.,  3.,  4.,\n",
       "        1.,  1.,  4.,  8.,  4.,  5.,  3.,  3.,  7.,  7.,  8.])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The *actual* class of test set\n",
    "y_dig_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted label</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual label</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted label   0   1  2  3   4   5   6   7   8   9\n",
       "Actual label                                         \n",
       "0                17   0  0  0   0   0   0   0   0   0\n",
       "1                 0  17  0  0   0   0   0   0   2   0\n",
       "2                 0   2  7  0   0   0   0   0   9   0\n",
       "3                 0   0  1  7   0   0   0   1   6   0\n",
       "4                 0   1  1  0  17   0   0   2   1   0\n",
       "5                 0   0  0  0   0  20   0   1   0   0\n",
       "6                 0   0  0  0   0   0  15   0   0   0\n",
       "7                 0   0  0  0   0   0   0  20   0   0\n",
       "8                 0   2  0  0   0   0   0   0  12   0\n",
       "9                 0   2  0  0   0   0   0   2   5  10"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the confusion matrix\n",
    "conf_dig = conf_matrix(y_dig_test, y_dig_predict)\n",
    "\n",
    "# Output the confusion matrix\n",
    "conf_dig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Naive Bayes Model Error Rate: 0.21\n"
     ]
    }
   ],
   "source": [
    "# When we were wrong, how wrong were we?\n",
    "# Error rate is the mean of how wrong our incorrect predictions were\n",
    "err_rate_dig_nb = (y_dig_predict != y_dig_test).mean()\n",
    "print('Naive Bayes Model Error Rate: %.2f' % err_rate_dig_nb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _k_-nearest Neighbors\n",
    "\n",
    "The next classifier is [k-nearest Neighbors](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Iris Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97037037037037033"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import k-nearest neighbors library\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "# Create the knn model object with 5 neighbors\n",
    "knn = KNeighborsClassifier(n_neighbors=5)\n",
    "\n",
    "# Train the model\n",
    "knn.fit(X_train, y_train)\n",
    "\n",
    "# Check the score\n",
    "knn.score(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  2.,  0.,  1.,  1.,  2.,  1.,  0.,  0.,  0.,  2.,  1.,\n",
       "        2.,  0.])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the class of test set\n",
    "y_predict = knn.predict(X_test)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  2.,  0.,  1.,  1.,  1.,  1.,  0.,  0.,  0.,  2.,  1.,\n",
       "        2.,  0.])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The *actual* class of test set\n",
    "y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted label</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual label</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted label  0  1  2\n",
       "Actual label            \n",
       "0                5  0  0\n",
       "1                0  5  1\n",
       "2                0  0  4"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the confusion matrix\n",
    "conf = conf_matrix(y_test, y_predict)\n",
    "\n",
    "# Output the confusion matrix\n",
    "conf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Naive Bayes Model Error Rate: 0.07\n"
     ]
    }
   ],
   "source": [
    "# When we were wrong, how wrong were we?\n",
    "# Error rate is the mean of how wrong our incorrect predictions were\n",
    "err_rate = (y_predict != y_test).mean()\n",
    "print('Naive Bayes Model Error Rate: %.2f' % err_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try running KNN with K values 1 to 10, measuring testing accuracy for each K and plotting results.\n",
    "\n",
    "Inspiration: https://github.com/justmarkham/scikit-learn-videos/blob/master/05_model_evaluation.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0vcyFwsyscb7qyczMMvXaGIWkP4+If5d0Bn/YohDJVU8XbEFOMzNrElmD2cPTz1vTwCR9\nZmbWv+QZozgoIu7rbl8Z3PVkZta4IiYFvLSLfZfkj2RmZs0sa4zij4E/AbaX9DWSsQlIuqIG9UE2\nMzOrgKwxiqG8URS2rtv/IvCnRYYyM7PqyDNGsWtE/Hf6eBDwtoh4oS/CdcdjFGZmjStijOIcSdtI\nGkGyXOkSSWf2OKGZmTWVPIVibES8CHwSuJ1kFtk/LzKUmZlVR55CMVjSEJJCcUtEbMD3VZiZDRh5\nCsXlwErgbcB/SBoDVGKMwszMitfwXE+SBAyKiI3FRGooiwezzcwa1OuD2ZJ2kDRd0sx0117AF3oa\n0MzMmkuerqcfAbOAHdPtx4DTiwpkZmbVstlCIal2M96oiPgp6TKo6WB26d1OZmbWN7JaFHPSzy9L\nGlXbKWkcHsw2MxswsqbwqA10nAH8EniPpAeA7fEUHmZmA8Zmr3qStAq4gKRgCNgq/fx74LUqLFzk\nq57MzBrXayvc8ebJAGuGd7HPzMz6qawWxfyI2K+P8zTELQozs8YVMSmgmZkNYFktiu0i4rk+ztMQ\ntyjMzBrXaIui4Sk8qsSFwsysce56MjOzXuVCYWZmmVwozMwskwuFmZllcqEwM7NMLhRmZpbJhcLM\nzDK5UJiZWSYXCjMzy+RCYWZmmVwozMwskwuFmZllKrRQSJooaZmkxyRN6eL5UZJmSnpY0iJJJ9Y9\nt1LSI5LmS5rT+VwzM+sbhc0eK2kQsByYADwNPAhMioildce0AVtFxFmSRqXHj46IjZKeBA6IiDUZ\nX8Ozx5qZNahKs8e2AI9HxMqI2ABcDxzb6ZjfANukj7cBnouIjXXP5/6HmJlZMYosFDsBT9Vtr0r3\n1bsCGCtpNbAAmFz3XAB3Spor6eQCc5qZWYbBBb52nj6hqcDDEdEqaTfgDkn7RsRLwPiI+I2k7dP9\nyyLi3s4v0NbW9vrj1tZWWltbeye9mVk/0dHRQUdHR4/PL3KMYhzQFhET0+2zgE0RcV7dMbcB34mI\n+9Ptu4ApETG302udDbwcEdM67fcYhZlZg6o0RjEX2F3SGElDgc8CMzods4xksBtJo4E9gSckDZe0\ndbp/BHAEsLDArGZmthmFdT2lVy6dCrQDg4DpEbFU0inp85cD3wWulrSApGidGRFrJL0HuElSLeM1\nETGrqKxmZrZ5hXU99QV3PZmZNa5KXU9mZtYPuFCYmVkmFwozM8vkQmFmZplcKMzMLJMLhZmZZXKh\nMDOzTC4UZmaWyYXCzMwyuVCYmVkmFwozM8vkQmFmZplcKMzMLJMLhZmZZXKhMDOzTC4UZmaWyYXC\nzMwyuVCYmVkmFwozM8vkQmFmZplcKMzMLJMLhZmZZXKhMDOzTC4UZmaWyYXCzMwyuVCYmVkmFwoz\nM8vkQmFmZplcKMzMLJMLhZmZZXKhMDOzTC4UZmaWyYXCzMwyuVCYmVkmFwozM8vkQmFmZplcKMzM\nLJMLhZmZZXKhMDOzTC4UZmaWyYXCzMwyFVooJE2UtEzSY5KmdPH8KEkzJT0saZGkE/Oea2ZmfaOw\nQiFpEPB9YCKwNzBJ0l6dDjsVmB8RHwRagWmSBuc8t5I6OjrKjtClKuZypnycKb8q5qpipkYV2aJo\nAR6PiJURsQG4Hji20zG/AbZJH28DPBcRG3OeW0lV/aGoYi5nyseZ8qtiripmalSRhWIn4Km67VXp\nvnpXAGMlrQYWAJMbONfMzPpAkYUichwzFXg4InYEPgj8QNLWBWYyM7MGKSLP+3kPXlgaB7RFxMR0\n+yxgU0ScV3fMbcB3IuL+dPsuYAowuLtz0/3FhDcz6+ciQnmPHVxgjrnA7pLGAKuBzwKTOh2zDJgA\n3C9pNLAn8ATwYo5zG/qHmplZzxRWKCJio6RTgXZgEDA9IpZKOiV9/nLgu8DVkhaQdIOdGRFrALo6\nt6isZma2eYV1PZmZWf/QlHdmS7pK0jOSFpadpUbSLpLulrQ4vXnwqxXI9FZJs9MbGpdIOqfsTDWS\nBkmaL+mWsrPUSFop6ZE015yy8wBIGinpRklL0//DcSXn2TP9/tQ+XqjIz/pZ6e/eQknXStqqApkm\np3kWSZrc/RmF5XjT+6Wkd0i6Q9KjkmZJGpn1Gk1ZKICrSW7Gq5INwOkRMRYYB/x12TcJRsQ64LD0\nhsYPAIdJOqjMTHUmA0vId3VcXwmgNSL2i4iWssOkLgZui4i9SP4PS+2CjYjl6fdnP+AA4HfAzWVm\nSscyTwb2j4h9SLqrTyg50/uBLwMfBvYFjpG0W0lxunq//DvgjojYA7gr3d6spiwUEXEv8HzZOepF\nxP9GxMPp45dJfqF3LDcVRMTv0odDSX6B1pQYBwBJOwNHA1cCVbsgoTJ5JG0LHBwRV0Ey7hcRL5Qc\nq94EYEVEPNXtkcV6keQPteGSBgPDgafLjcT7gNkRsS4iXgPuAY4vI8hm3i8/Afw4ffxj4JNZr9GU\nhaLq0r9w9gNml5sEJL1F0sPAM8DdEbGk7EzAhcDXgU1lB+kkgDslzZV0ctlhgHcDz0q6WtI8SVdI\nGl52qDonANeWHSK9AGYa8D8kV0mujYg7y03FIuDgtItnOPAxYOeSM9UbHRHPpI+fAUZnHexC0csk\nvQ24EZictixKFRGb0q6nnYFDJLWWmUfSMcBvI2I+FfrrPTU+7VI5iqTr8OCS8wwG9gd+GBH7A6/Q\nTRdBX5E0FPg48LMKZNkNOA0YQ9KKf5ukz5WZKSKWAecBs4DbgflU7w8jACK5oimzC9iFohdJGgL8\nHPhJRPyi7Dz10i6LXwEfKjnKnwCfkPQkcB1wuKR/KzkTABHxm/TzsyT97mWPU6wCVkXEg+n2jSSF\nowqOAh5Kv1dl+xDwQETU5oq7ieTnrFQRcVVEfCgiDgXWAsvLzlTnGUk7AEh6F/DbrINdKHqJJAHT\ngSURcVHZeeD1adxHpo+HAR8l+cumNBExNSJ2iYh3k3Rd/DoiPl9mJgBJw2vTx0gaARwBlHpVXUT8\nL/CUpD3SXROAxSVGqjeJpNBXwTJgnKRh6e/hBJILJUol6Z3p5z8CjqMC3XR1ZgBfSB9/Acj8w7bI\nO7MLI+k64FBgO0lPAd+IiKtLjjUe+DPgEUm1N+OzImJmiZneBfxY0ltI/ij494i4q8Q8XanKVU+j\ngZuT9xkGA9dExKxyIwHwN8A1aVfPCuCkkvPUCukEkiuNShcRC9JW6VyS7p15wL+WmwqAGyVtRzLQ\n/pWIeLGMEHXvl6Nq75fAucANkr4ErAQ+k/kavuHOzMyyuOvJzMwyuVCYmVkmFwozM8vkQmFmZplc\nKMzMLJMLhZmZZXKhsAFB0st1j4+WtFzSLp2OOVHSa5L2qdu3KL1hKuu1r+hupmBJP5L0qS72t1Zp\nqnWzrrhQ2EARAJI+QjJ198TNzHq6Cvj7zudlvnDEyTlWYCzkhqX0ZkqzQvmHzAYMSYeQ3LH7sYh4\nsotDArgVGFs3bUb9+UdIekDSQ5JuSO9QRlKHpAPSx19KWyuz05bGpXUvcYik+yWt6NS62EbSrZKW\nSbosnYYCSZOULKS0UNK5dTlelvTP6azAfyzp3HTRngWSvrel3yezzlwobKB4K8lEf8dGxKMZx20C\nzgem1u+UNIqkpfGRiDgAeAj4Wvp0ACFpR+AfgANJpnTZkzdaEgJ2iIjxwDEkUyjUtACnAnsDuwHH\np691LnAY8EHgw5KOTY8fDvxXOivwMuCTETE2IvYFvp3/W2KWjwuFDRTrgftJVh3rzrUkk8yNqds3\njuSN/IF0Lq/PA/VjFyJ5w78nItams5j+jDemUg/SidfSbqr6+f/nRMTKiNhEMtHeQSQzonakM6K+\nBlwDHJIe/xrJLMUALwDrJE2XdBzwao5/n1lDXChsoNhEMvFZi6Szsg5M35in8cbaD7U3+ztqy4Cm\nf8F3nhSv8zhE5/U21m/muei0v6vxjPr969I1BEgLUgvJFOTHAGVOQmn9lAuFDRjpGuIfAz4n6Ytd\nHFL/5v0jkhlStyd5g54NjK+teyxphKTd618eeBA4VNLIdEnOT5FvELtF0ph0YPozwL3AnPS1tpNU\nWwP6njcFTsZJRkbE7SRdYfvm+HpmDWnKacbNeqD2F/jzkiYC/yHptxFxa6djasdtkHQxcFG6/ayk\nE4HrJG2VHv/3wGOvnxyxWtJ3Sd7k15CMH9SvcR1dPK4VmO8D7yVZn+NmAEl/B9xNUsBujYhbunid\nrYFfSnpretzpDX1XzHLwNONmvUjSiIh4JW1R3ARMj4hflp3LbEu468msd7Wlg90LgSdcJKw/cIvC\nzMwyuUVhZmaZXCjMzCyTC4WZmWVyoTAzs0wuFGZmlsmFwszMMv0/JCluY8dw4EoAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2a668ec950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import metrics library\n",
    "from sklearn import metrics\n",
    "\n",
    "# Increase k from 1 to 10\n",
    "k_range = range(1, 11)\n",
    "scores = []\n",
    "for k in k_range:\n",
    "    knn = KNeighborsClassifier(n_neighbors=k)\n",
    "    knn.fit(X_train, y_train)\n",
    "    y_predict = knn.predict(X_test)\n",
    "    scores.append(metrics.accuracy_score(y_test, y_predict))\n",
    "\n",
    "# Plot results\n",
    "plt.plot(k_range, scores, color='blue')\n",
    "plt.scatter(k_range, scores, color='red')\n",
    "\n",
    "plt.ylim([0.8,1.02])\n",
    "plt.xlim([1.0,10.0])\n",
    "plt.xlabel('K Neighbors')\n",
    "plt.ylabel('Testing Accuracy')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Digits Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99010513296227587"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the knn model object with 5 neighbors\n",
    "knn_dig = KNeighborsClassifier(n_neighbors=5)\n",
    "\n",
    "# Train the model\n",
    "knn_dig.fit(X_dig_train, y_dig_train)\n",
    "\n",
    "# Check the score\n",
    "knn_dig.score(X_dig_train, y_dig_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.,  6.,  1.,  7.,  4.,  1.,  4.,  7.,  0.,  1.,  5.,  6.,  2.,\n",
       "        7.,  8.,  4.,  9.,  0.,  9.,  0.,  5.,  2.,  2.,  4.,  1.,  8.,\n",
       "        8.,  7.,  2.,  9.,  7.,  0.,  0.,  6.,  0.,  5.,  0.,  5.,  1.,\n",
       "        0.,  8.,  6.,  6.,  0.,  3.,  4.,  0.,  3.,  5.,  6.,  9.,  8.,\n",
       "        4.,  8.,  5.,  2.,  7.,  5.,  5.,  1.,  1.,  8.,  9.,  0.,  3.,\n",
       "        4.,  9.,  2.,  9.,  7.,  1.,  7.,  5.,  4.,  9.,  5.,  7.,  7.,\n",
       "        7.,  0.,  1.,  9.,  1.,  9.,  7.,  1.,  3.,  9.,  4.,  9.,  2.,\n",
       "        5.,  3.,  5.,  6.,  2.,  3.,  0.,  7.,  3.,  2.,  5.,  2.,  6.,\n",
       "        1.,  7.,  0.,  2.,  9.,  4.,  2.,  0.,  7.,  4.,  4.,  9.,  0.,\n",
       "        4.,  9.,  6.,  8.,  2.,  6.,  4.,  4.,  9.,  1.,  2.,  4.,  7.,\n",
       "        8.,  8.,  2.,  2.,  5.,  9.,  5.,  4.,  3.,  1.,  4.,  7.,  1.,\n",
       "        5.,  3.,  8.,  6.,  5.,  5.,  2.,  1.,  0.,  9.,  1.,  6.,  9.,\n",
       "        3.,  7.,  4.,  5.,  6.,  3.,  6.,  5.,  2.,  7.,  6.,  3.,  4.,\n",
       "        1.,  1.,  4.,  8.,  4.,  5.,  3.,  3.,  7.,  7.,  8.])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict the class of test set\n",
    "y_dig_predict = knn_dig.predict(X_dig_test)\n",
    "y_dig_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8.,  6.,  1.,  7.,  4.,  1.,  4.,  7.,  0.,  1.,  5.,  6.,  2.,\n",
       "        7.,  8.,  4.,  9.,  0.,  9.,  0.,  5.,  2.,  2.,  4.,  1.,  8.,\n",
       "        8.,  7.,  2.,  9.,  7.,  0.,  0.,  6.,  0.,  5.,  0.,  5.,  1.,\n",
       "        0.,  8.,  6.,  6.,  0.,  3.,  4.,  0.,  3.,  5.,  6.,  9.,  8.,\n",
       "        4.,  8.,  5.,  2.,  7.,  5.,  5.,  1.,  1.,  8.,  9.,  0.,  3.,\n",
       "        4.,  9.,  2.,  9.,  3.,  1.,  7.,  5.,  4.,  9.,  5.,  7.,  7.,\n",
       "        7.,  0.,  1.,  9.,  1.,  9.,  7.,  1.,  3.,  9.,  4.,  9.,  2.,\n",
       "        5.,  3.,  5.,  6.,  2.,  3.,  0.,  7.,  3.,  2.,  5.,  2.,  6.,\n",
       "        1.,  7.,  0.,  2.,  9.,  4.,  2.,  0.,  7.,  4.,  4.,  9.,  0.,\n",
       "        4.,  9.,  6.,  8.,  2.,  6.,  4.,  4.,  9.,  1.,  2.,  4.,  7.,\n",
       "        8.,  8.,  2.,  2.,  5.,  9.,  5.,  4.,  3.,  1.,  4.,  7.,  1.,\n",
       "        5.,  3.,  8.,  6.,  5.,  5.,  2.,  1.,  0.,  9.,  1.,  6.,  9.,\n",
       "        3.,  7.,  4.,  5.,  6.,  3.,  6.,  5.,  2.,  7.,  6.,  3.,  4.,\n",
       "        1.,  1.,  4.,  8.,  4.,  5.,  3.,  3.,  7.,  7.,  8.])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The *actual* class of test set\n",
    "y_dig_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted label</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual label</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>21</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted label   0   1   2   3   4   5   6   7   8   9\n",
       "Actual label                                           \n",
       "0                17   0   0   0   0   0   0   0   0   0\n",
       "1                 0  19   0   0   0   0   0   0   0   0\n",
       "2                 0   0  18   0   0   0   0   0   0   0\n",
       "3                 0   0   0  14   0   0   0   1   0   0\n",
       "4                 0   0   0   0  22   0   0   0   0   0\n",
       "5                 0   0   0   0   0  21   0   0   0   0\n",
       "6                 0   0   0   0   0   0  15   0   0   0\n",
       "7                 0   0   0   0   0   0   0  20   0   0\n",
       "8                 0   0   0   0   0   0   0   0  14   0\n",
       "9                 0   0   0   0   0   0   0   0   0  19"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the confusion matrix\n",
    "conf_dig = conf_matrix(y_dig_test, y_dig_predict)\n",
    "\n",
    "# Output the confusion matrix\n",
    "conf_dig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Naive Bayes Model Error Rate: 0.01\n"
     ]
    }
   ],
   "source": [
    "# When we were wrong, how wrong were we?\n",
    "# Error rate is the mean of how wrong our incorrect predictions were\n",
    "err_rate_dig_nb = (y_dig_predict != y_dig_test).mean()\n",
    "print('Naive Bayes Model Error Rate: %.2f' % err_rate_dig_nb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try running KNN with K values 1 to 10, measuring testing accuracy for each K and plotting results.\n",
    "\n",
    "Inspiration: https://github.com/justmarkham/scikit-learn-videos/blob/master/05_model_evaluation.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qi4xH0knAXyNiKjX07T11eNqk8nGSpsMjC46nO3AI8IOIOARYQStNBB1FUk/g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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2a65a94b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import metrics library\n",
    "from sklearn import metrics\n",
    "\n",
    "# Increase k from 1 to 10\n",
    "k_range = range(1, 11)\n",
    "scores_dig = []\n",
    "for k in k_range:\n",
    "    knn_dig = KNeighborsClassifier(n_neighbors=k)\n",
    "    knn_dig.fit(X_dig_train, y_dig_train)\n",
    "    y_dig_predict = knn_dig.predict(X_dig_test)\n",
    "    scores_dig.append(metrics.accuracy_score(y_dig_test, y_dig_predict))\n",
    "\n",
    "# Plot results\n",
    "plt.plot(k_range, scores_dig, color='blue')\n",
    "plt.scatter(k_range, scores_dig, color='red')\n",
    "\n",
    "plt.ylim([0.95,1.02])\n",
    "plt.xlim([1.0,10.0])\n",
    "plt.xlabel('K Neighbors')\n",
    "plt.ylabel('Testing Accuracy')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Forests\n",
    "\n",
    "Finally, we will consider the [Random Forests](https://en.wikipedia.org/wiki/Random_forest) ensemble classifier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random Forest Cross-validation Scores: [ 1.          0.93333333  1.          0.93333333  0.93333333  1.\n",
      "  0.86666667  0.93333333  1.          1.        ]\n"
     ]
    }
   ],
   "source": [
    "# Import the Random Forests library\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "# Create the Random Forest model object with 5 neighbors\n",
    "rf = RandomForestClassifier()\n",
    "\n",
    "# Evaluate using 10-fold cross-validation\n",
    "scores = cross_validation.cross_val_score(rf, iris.data, iris.target, cv=10)\n",
    "\n",
    "# Display the individual CV scores\n",
    "print 'Random Forest Cross-validation Scores:', scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rhQ49KVGISP7q6sIQFMDgwUoSZUqJQkREYml5rIiIFJUShYiIxFKiEBGRWEoU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\nlhKFiIjEUqIQEZFYShQiIhLr/wDWZ7lNxkf8OAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2a5c645950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot fold scores\n",
    "folds = range(1, 11)\n",
    "folds = np.array(folds)\n",
    "\n",
    "plt.xlabel('Fold')\n",
    "plt.ylabel('Score')\n",
    "plt.ylim([0.8,1.02])\n",
    "plt.xlim([1.0,10.0])\n",
    "\n",
    "plt.scatter(folds, scores, color='red')\n",
    "plt.plot(folds, scores, color='blue')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean SVM Cross-validation Score: 0.96\n"
     ]
    }
   ],
   "source": [
    "# Mean CV evaluation score\n",
    "print 'Mean SVM Cross-validation Score:', scores.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Digits Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random Forest Cross-validation Scores: [ 0.85405405  0.94535519  0.91160221  0.89444444  0.91061453  0.95530726\n",
      "  0.93854749  0.9494382   0.91525424  0.90340909]\n"
     ]
    }
   ],
   "source": [
    "# Create the Random Forest model object with 5 neighbors\n",
    "rf_dig = RandomForestClassifier()\n",
    "\n",
    "# Evaluate using 10-fold cross-validation\n",
    "scores_dig = cross_validation.cross_val_score(rf_dig, digits.data, digits.target, cv=10)\n",
    "\n",
    "# Display the individual CV scores\n",
    "print 'Random Forest Cross-validation Scores:', scores_dig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fYBRQH3jA3WeY2XnR4/cBfwIeMrNphND6rbsvMbPdgCFmVl7jo+6uiRIiIiko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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2a5c1affd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot fold scores\n",
    "folds_dig = range(1, 11)\n",
    "folds_dig = np.array(folds)\n",
    "\n",
    "plt.xlabel('Fold')\n",
    "plt.ylabel('Score')\n",
    "plt.ylim([0.8,1.02])\n",
    "plt.xlim([1.0,10.0])\n",
    "\n",
    "plt.scatter(folds_dig, scores_dig, color='red')\n",
    "plt.plot(folds_dig, scores_dig, color='blue')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean SVM Cross-validation Score: 0.917802670389\n"
     ]
    }
   ],
   "source": [
    "# Mean CV evaluation score\n",
    "print 'Mean SVM Cross-validation Score:', scores_dig.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And that's it.\n",
    "\n",
    "If you are interested, you could go back and change code to better evaluate the accuracy (relative and absolute) of the models, but I'll leave that for another time.\n",
    "\n",
    "Cheers!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}