Sorry about my last two blank comments. Mouse double-click errors.
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Very nice code! However I have a couple of subtle comments:
1) When you center the Kernel matrix be sure to divide the 'ones' matrix by the number of samples i.e.
Line 43: one_mat = ones(size(K));
should read
Line 43: one_mat = ones(size(K))./size(data_in,2);
Line 43: one_mat = ones(size(K));
should read
Line 43: one_mat = ones(size(K))./size(data_in,2);
2) Eigenvector normalization implies dividing each of the columns of the eigenvector matrix by the sqrt of its corresponding eigenvalue. Do so by substituting:
Line 61: eigvec(:,col) = eigvec(:,col)./(sqrt(eig_val(col,col)));
to read
Line 61: eigvec(:,col) = eigvec(:,col)./(sqrt(eigval(col,col)));
Line 61: eigvec(:,col) = eigvec(:,col)./(sqrt(eig_val(col,col)));
to read
Line 61: eigvec(:,col) = eigvec(:,col)./(sqrt(eigval(col,col)));
3) Also, if you must do eigenvalue sorting, be careful to use only the diagonal of the 'Lambda' matrix and not the whole matrix. Use:
Line 63: [dummy, index] = sort(diag(eigval),'descend');
instead of
Line 63: [dummy, index] = sort(eig_val,'descend');
instead of
Line 63: [dummy, index] = sort(eig_val,'descend');
You can also see 'Learning with Kernels' by B. Scholkopf and A. Smola, Section 14.2 (particularly eqs 14.14 and 14.17). Hope this is helpful.