Explore the Relationship Between Number Principal Components and Accuracy

Context and Summary

This is code extends eigenfaces2020 by systematically varying the number of principal components used in the Eigenfaces algorithm. The students do this exercise as part of their Night 7 assignment.

Source Code Listing

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function accuracy = eigenfaces2020(numPrincipalComponents, useOnlyNoSmileForTraining, showEigenFaces)
% handy trick to set a default values for our arguments
if nargin < 1
    numPrincipalComponents = 10;
end
if nargin < 2
    % this is true to use the data in part 7
    useOnlyNoSmileForTraining = false;
end
if nargin < 3
    showEigenFaces = false;
end

if ~useOnlyNoSmileForTraining
    load('classdata_train.mat');
    load('classdata_test.mat');
else
    load('classdata_no_smile.mat');
    load('classdata_smile.mat');
end

ATrain = reshape(grayfaces_train, [size(grayfaces_train,1)*size(grayfaces_train,2), size(grayfaces_train,3)])';
ATest = reshape(grayfaces_test, [size(grayfaces_test,1)*size(grayfaces_test,2), size(grayfaces_test,3)])';

% mean center the train and test data
ATrain = ATrain - mean(ATrain);
ATest = ATest - mean(ATest);

% get covariance matrix of the training data
covar = ATrain'*ATrain;

% get EVD (so we can do PCA)
% If you want all of the Eigenvectors / Eigenvalue, you can use eig:
% [Q, Delta] = eig(covar);

% if you wan to just get the eigenvectors swith largest eigenvalues
% you can use eigs.
[Q, Delta] = eigs(covar, numPrincipalComponents);

if showEigenFaces
    % visualize the principal components as images
    f = figure;
    for i = 1 : numPrincipalComponents
        subplot(ceil(sqrt(numPrincipalComponents)), ceil(sqrt(numPrincipalComponents)), i);
        imagesc(reshape(Q(:,i), [64 64]));  % TODO: remove hardcoding
        colormap('gray');
    end
end

% project into face space
faceSpaceTrain = Q'*ATrain';
faceSpaceTest = Q'*ATest';

% Use nearest neighbor search (you can code this manually if you'd like)
NN = knnsearch(faceSpaceTrain', faceSpaceTest');

% let's check to see if the subject corresponding to the second closest
% photo is the same as the one corresponding to the query image
accuracy = mean(subject_train(NN)==subject_test);
end