How to get four faces with the highest eigenvalue​s/eigenvec​tors?

I'm trying to understand eigenfaces. I've a dataset with X faces as rows, and X datapoints as columns.

I've already turned this datafile into a covariance matrix, and now I want to make a graph with the two faces with the highest eigenvalues and the two faces with the lowest eigenvalues.

How to do this? I now have:

• covmat = cov(faces)
• [V,D] = eig(covmat)
• high = eigs(D,2)
• low = eigs(D,2,'smallestabs')

I now have the highest and lowest numbers in the D-matrix (highest and lowest eigenvalues). But how do I transpose this back to faces? How to know which eigenvalue corresponds to which face? And how to display them in a figure?

Thanks for thinking along!!

Answer 1

[Shubham]

Hi Eline,

To display the faces corresponding to the highest and lowest eigenvalues in your dataset, follow these steps:

1. Compute the covariance matrix:

covmat = cov(faces);

2. Use the eig function to calculate Eigenvectors and Eigenvalues:

[V, D] = eig(covmat);

3. Extract the Eignevalues from diagonal of D and sort them to find the indices of the highest and lowest values.

eigenvalues = diag(D);
[sortedEigenvalues, indices] = sort(eigenvalues, 'descend');

4. Use the indices to select the corresponding Eigenvectors for the highest and lowest Eigenvalues:

topEigenvectors = V(:, indices(1:2));  % Two largest eigenvectors
bottomEigenvectors = V(:, indices(end-1:end));  % Two smallest eigenvectors

5. Assuming each face is a square image, reshape the Eigenvectors to the original image dimensions and display them:

% Assuming each face is a square image of size sqrt(N) x sqrt(N)
faceSize = sqrt(size(faces, 2));

figure;

% Reshape and display the top eigenfaces
subplot(2, 2, 1);
imshow(reshape(topEigenvectors(:, 1), [faceSize, faceSize]), []);
title('Top Eigenface 1');

subplot(2, 2, 2);
imshow(reshape(topEigenvectors(:, 2), [faceSize, faceSize]), []);
title('Top Eigenface 2');

% Reshape and display the bottom eigenfaces
subplot(2, 2, 3);
imshow(reshape(bottomEigenvectors(:, 1), [faceSize, faceSize]), []);
title('Bottom Eigenface 1');

subplot(2, 2, 4);
imshow(reshape(bottomEigenvectors(:, 2), [faceSize, faceSize]), []);
title('Bottom Eigenface 2');

For more information, refer to the following documentation links:

• cov: https://mathworks.com/help/releases/R2024b/matlab/ref/cov.html
• eig: https://mathworks.com/help/releases/R2024b/matlab/ref/eig.html

Hope this helps.