**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 It is superseded by a new package MultivariateStats.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)
X each represent a data point (i.e., a different repetition of the experiment),
and columns of
X represent the different variables measured.
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
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
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.
scale is true (default), then the principal components of the data are also
scaled back to the original space and saved to
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 + weight * [0, PCs[1,v]], ctr + 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.