Created
June 15, 2012 19:48
distance covariance and correlation
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| # -*- coding: utf-8 -*- | |
| """ | |
| Created on Fri Jun 15 14:00:29 2012 | |
| Author: Josef Perktold | |
| License: MIT, BSD-3 (for statsmodels) | |
| http://en.wikipedia.org/wiki/Distance_correlation | |
| Yaroslav and Satrajit on sklearn mailing list | |
| Univariate only, distance measure is just absolute distance | |
| Note: Same as R package energy DCOR, except DCOR reports sqrt of all returns of dcov_all | |
| """ | |
| import numpy as np | |
| def dist(x, y): | |
| #1d only | |
| return np.abs(x[:, None] - y) | |
| def d_n(x): | |
| d = dist(x, x) | |
| dn = d - d.mean(0) - d.mean(1)[:,None] + d.mean() | |
| return dn | |
| def dcov_all(x, y): | |
| dnx = d_n(x) | |
| dny = d_n(y) | |
| denom = np.product(dnx.shape) | |
| dc = (dnx * dny).sum() / denom | |
| dvx = (dnx**2).sum() / denom | |
| dvy = (dny**2).sum() / denom | |
| dr = dc / (np.sqrt(dvx) * np.sqrt(dvy)) | |
| return dc, dr, dvx, dvy | |
| import matplotlib.pyplot as plt | |
| fig = plt.figure() | |
| for case in range(1,5): | |
| np.random.seed(9854673) | |
| x = np.linspace(-1,1, 501) | |
| if case == 1: | |
| y = - x**2 + 0.2 * np.random.rand(len(x)) | |
| elif case == 2: | |
| y = np.cos(x*2*np.pi) + 0.1 * np.random.rand(len(x)) | |
| elif case == 3: | |
| x = np.sin(x*2*np.pi) + 0.0 * np.random.rand(len(x)) #circle | |
| elif case == 4: | |
| x = np.sin(x*1.5*np.pi) + 0.1 * np.random.rand(len(x)) #bretzel | |
| dc, dr, dvx, dvy = dcov_all(x, y) | |
| print dc, dr, dvx, dvy | |
| ax = fig.add_subplot(2,2, case) | |
| #ax.set_xlim(-1, 1) | |
| ax.plot(x, y, '.') | |
| yl = ax.get_ylim() | |
| ax.text(-0.95, yl[0] + 0.9 * np.diff(yl), 'dr=%4.2f' % dr) | |
| plt.show() |
@nickhsmith: Format your inputs as arrays like so:
x = np.array([5.1, 5.3, 5.2, ...])
y = np.array([7.0, 6.8, 7.2, ...])
Hi, where you have in line 41
dr = dc / (np.sqrt(dvx) * np.sqrt(dvy))I believe it should be
dr = np.sqrt(dc) / np.sqrt(np.sqrt(dvx) * np.sqrt(dvy))
This code is hard to understand
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What python version are you running? And what exactly would the inputs be? I have 2 lists of floats (x,y) x =[5.1,5.3,5.2 ...] and y = [7.0,6.8,7.2 ...] should I use those as the input?
I'm using 2.7 and getting an error on the distance method. x[:, None] gives me the error TypeError: list indices must be integers, not tuple
Thanks