https://github.com/JuliaStats/DimensionalityReduction.jl

Deprecated in favor of MultivariateStats.jl
https://github.com/JuliaStats/DimensionalityReduction.jl

Last synced: 3 months ago
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Deprecated in favor of MultivariateStats.jl

• Host: GitHub
• URL: https://github.com/JuliaStats/DimensionalityReduction.jl
• Owner: JuliaStats
• License: other
• Archived: true
• Created: 2012-12-22T16:55:51.000Z (almost 12 years ago)
• Default Branch: master
• Last Pushed: 2014-09-13T16:21:15.000Z (about 10 years ago)
• Last Synced: 2024-06-28T04:34:03.601Z (4 months ago)
• Language: Julia
• Homepage:
• Size: 572 KB
• Stars: 27
• Watchers: 22
• Forks: 20
• Open Issues: 5
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

Awesome Lists containing this project

• awesome-julia-datasciences - Dimensionality Reduction - Methods for dimensionality reduction. (APL / General-Purpose Machine Learning)

README

        
DimensionalityReduction.jl

==========================

**The DimensionalityReduction package is deprecated. It is superseded by a new package [MultivariateStats](https://github.com/JuliaStats/MultivariateStats.jl). **.

---

# Algorithms

* Principal Component Analysis (PCA)

# PCA Usage

    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](https://github.com/stevengj/PyPlot.jl)

	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](https://github.com/stevengj/PyPlot.jl)

	using PyPlot

	scores = Xpca.scores[:,1:2]

	plot( scores[:,1], scores[:,2], "r." )

To make a biplot with [Gadfly](http://dcjones.github.io/Gadfly.jl/):

    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

ICA has been deprecated.

# t-SNE Usage

t-SNE has been deprecated.

# NMF

NMF has been moved into a separate [package](https://github.com/JuliaStats/NMF.jl).