Principle Component Analysis Computation
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Hi all I am applying Principle Component Analysis manauall. I have a Dataset let say
Data= [2.5000 2.4000
0.5000 0.7000
2.2000 2.9000
1.9000 2.2000
3.1000 3.0000
2.3000 2.7000
2.0000 1.6000
1.0000 1.1000
1.5000 1.6000
1.1000 0.9000]
when I compute directly by calling the matlab function princomp I get the PC
0.6779 0.7352
0.7352 -0.6779
But when I do manually like that
function [V newX D] = Untitled(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
0.6779 -0.7352
0.7352 0.6779
I am getting different result just the minis difference why is it/
Thanks in Advance.
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Leah
le 23 Avr 2013
they are the same because the eigenvector (-.7532 0.6779) is equivalent to (.7532 -0.6779)
3 commentaires
Matt Kindig
le 23 Avr 2013
They are equal because, by definition, all elements of an eigenvector can be scaled by an arbitrary constant without changing the eigenvector. This is a property of eigenvectors. If (-0.7532, 0.6779) is scaled by -1, it gives (0.7532, -0.6779).
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