Principal Component Analysis in Ruby

pca.rb

# Ruby implementation of PCA as described in:
#
#   A tutorial on Principal Components Analysis
#   Lindsay I Smith February 26, 2002
#   http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf
# 
# Install:
#
#   brew install gsl
#   brew install gnuplot --with-x11
#   gem instal rb-gsl gnuplot

require 'gsl'
require 'gnuplot'

# Step 1: Get some data
m = GSL::Matrix[
  [2.5, 2.4],
  [0.5, 0.7],
  [2.2, 2.9],
  [1.9, 2.2],
  [3.1, 3.0],
  [2.3, 2.7],
  [2.0, 1.6],
  [1.0, 1.1],
  [1.5, 1.6],
  [1.1, 0.9]
]

p m

# Step 2: Subtract the mean
m.size2.times do |i|
  m.col(i).sub! m.col(i).mean
end

p m

Gnuplot.open do |gp|
  Gnuplot::Plot.new(gp) do |plot|
    plot.title "Mean adjusted data"
    plot.terminal "png"
    plot.output "mean.png"

    plot.data << Gnuplot::DataSet.new([m.col(0).to_a, m.col(1).to_a]) do |ds|
      ds.notitle
    end
  end
end

`open mean.png`


# Step 3: Calculate the covariance matrix
cov = (m.transpose * m) / (m.size1 - 1)
p cov

# Step 4: Calculate the eigenvectors and eigenvalues of the covariance matrix

eigval, eigvec = cov.eigen_symmv

p eigval, eigvec


# Step 5: Choosing components and forming a feature vector

sorted_vecs = eigval.sort_index.to_a.map {|i| eigvec.col(i) }.reverse
feature_vec = GSL::Matrix[*sorted_vecs].transpose
p feature_vec


# Step 5: Deriving the new data set

final = feature_vec.transpose * m.transpose

transformed = final.transpose

p transformed


Gnuplot.open do |gp|
  Gnuplot::Plot.new(gp) do |plot|
    plot.title "Transformed data"
    plot.terminal "png"
    plot.output "transformed.png"

    plot.data << Gnuplot::DataSet.new([transformed.col(0).to_a, transformed.col(1).to_a]) do |ds|
      ds.notitle
    end
  end
end

`open transformed.png`

Created a gem for this: https://github.com/gbuesing/pca