DimensionalityReduction.jl

Algorithms

• Principal Component Analysis (PCA)
• Independant Component Analysis (ICA)
• Non-negative Matrix Factorization (NMF)
• t-Distributed Stochastic Neighbor Embedding (t-SNE)

PCA Usage

using DimensionalityReduction

X = reshape(rand(40),10,4)
Xpca = pca(X)

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.

To make a biplot:

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 Usage

using DimensionalityReduction

# Generate true sources
S_true = rand(5,1000)

# Mixing matrix
H_true = randn(5, 5)

# generate observed signals
X = H_true*S_true

results = ica(X)

NMF Usage

using DimensionalityReduction

X = hcat(eye(2), eye(2))
X = vcat(X, X, X, X)
results = nmf(X, 2)

t-SNE Usage

using DimensionalityReduction

X = hcat(eye(2), eye(2))
X = vcat(X, X, X, X)
results = tsne(X, 2)