csci5521/assignments/hwk02/ProportionOfVariance.m

% implements Param_Est, returns the number of eigenvectors needed to
% explain 90% of the variance in the data, and displays a plot where the
% x-axis is the number of eigenvectors and the y-axis is the percentage of
% variance explained.
function [neigenvectors] = ProportionOfVariance(training_data)

  % stack data
  data = vertcat(training_data);

  % perform PCA
  [~,~,latent] = pca(data);

  % compute proportion of variance explained
  all_eigs = sum(latent);
  prop_var = cumsum(latent) / all_eigs;

  % show figure of proportion of variance explained where the x-axis is the number of eigenvectors and the y-axis is the percentage of
  % variance explained
  subplot(2,1,1);
  plot(find(latent), latent);

  subplot(2,1,2);
  plot(find(prop_var), prop_var);

  neigenvectors = find(prop_var > 0.9, 1);

end % Function end