% implements the Back Projection algorithm, returns nothing but displays
% the first 5 eigenfaces of the training data after being 'back-projected'
% using the first 10, 50, and 100 eigenvectors of the data.
function [] = Back_Project(training_data, test_data, n_components)
  
  % stack data 
  data = vertcat(training_data, test_data);

  % perform PCA
  [coeff, score] = pca(data);
   
  % for each number of principal components
  for n_idx = 1:length(n_components)
    n = n_components(n_idx);

    % perform the back projection algorithm using the first n_components(n) principal components
    W = coeff(:,1:n);
    z = score(:,1:n);
    sample_mean = mean(data);
    reconstruction = W * z' + sample_mean';

    % plot first 5 images back projected using the first
    % n_components(n) principal components
    for i = 1:5
      subplot(3,2,i)
      imagesc(reshape(reconstruction(:,i),32,30)');
    end

  end

end % Function end