Principle Component Analysis Computation

Question

Algorithms Analyst 2013-4-23

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/73251-principle-component-analysis-computation

Hi all I am applying Principle Component Analysis manauall. I have a Dataset let say

Data= [2.5000 2.4000

5000    0.7000
2000    2.9000
9000    2.2000
1000    3.0000
3000    2.7000
0000    1.6000
0000    1.1000
5000    1.6000
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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Answer 1

Leah 2013-4-23

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https://ww2.mathworks.cn/matlabcentral/answers/73251-principle-component-analysis-computation#answer_83221

they are the same because the eigenvector (-.7532 0.6779) is equivalent to (.7532 -0.6779)

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Matt Kindig 2013-4-23

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).

Algorithms Analyst 2013-4-28