**The DimensionalityReduction package is deprecated. It is superseded by a new package MultivariateStats. **.
- Principal Component Analysis (PCA)
using DimensionalityReduction
# simulate 100 random observations
# rotate and scale as well
X = randn(100,2) * [0.8 0.7; 0.9 0.5]
Xpca = pca(X)
Rows of X each represent a data point (i.e., a different repetition of the experiment),
and columns of X represent the different variables measured.
Attributes:
Xpca.rotation # principal components
Xpca.scores # rotated X
Xpca.standard_deviations # square roots of the eigenvalues
Xpca.proportion_of_variance # fraction of variance brought by each principal component
Xpca.cumulative_variance # cumulative proportion of variance
By default, pca() uses SVD decomposition. Alternatively, pcaeig(X) will calculate
directly the eigenvectors of the covariance matrix.
pca() centers and re-scales input data by default.
This is controlled by the center and scale keyword arguments:
pca(X::Matrix ; center::Bool, scale::Bool)
Centering is done by subtracting the mean, and scaling by normalizing each variable by its standard deviation.
If scale is true (default), then the principal components of the data are also
scaled back to the original space and saved to Xpca.rotation
To overlay the principal components on top of the data with PyPlot
using PyPlot
plot( X[:,1], X[:,2], "r." ) # point cloud
# get data center
ctr = mean( X, 1 )
# plot principal components as lines
# weight by their standard deviation
PCs = Xpca.rotation
for v=1:2
weight = Xpca.standard_deviations[v]
plot( ctr[1] + weight * [0, PCs[1,v]],
ctr[2] + weight * [0, PCs[2,v]],
linewidth = 2)
end
To make a biplot with PyPlot
using PyPlot
scores = Xpca.scores[:,1:2]
plot( scores[:,1], scores[:,2], "r." )
To make a biplot with Gadfly:
using Gadfly
scores = Xpca.scores[:,1:2]
pl = plot(x=scores[:,1],y=scores[:,2], Geom.point)
draw(PNG("pca.png", 6inch, 6inch), pl)
Starting from a DataFrame:
using RDatasets
iris = data("datasets", "iris")
iris = convert(Array,DataArray(iris[:,1:4]))
Xpca = pca(iris)
ICA has been deprecated.
t-SNE has been deprecated.
NMF has been moved into a separate package.