Principal Component Analysis in MATLAB

Question

I\'m implementing PCA using eigenvalue decomposition for sparse data. I know matlab has PCA implemented, but it helps me understand all the technicalities when I write code.

Answer 1

Here's how I would do it:

function [V newX D] = myPCA(X)
    X = bsxfun(@minus, X, mean(X,1));           %# zero-center
    C = (X'*X)./(size(X,1)-1);                  %'# cov(X)

    [V D] = eig(C);
    [D order] = sort(diag(D), 'descend');       %# sort cols high to low
    V = V(:,order);

    newX = X*V(:,1:end);
end

and an example to compare against the PRINCOMP function from the Statistics Toolbox:

load fisheriris

[V newX D] = myPCA(meas);
[PC newData Var] = princomp(meas);

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You might also be interested in this related post about performing PCA by SVD.