Principle Component Analysis Computation

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.

Answer 1

[Leah]

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

[Algorithms Analyst]

can you prove that how they are equal?

[Matt Kindig]

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]

If I use the princomp function in matlab using 2D image (grayscale image)

[A B C D]=princomp(img);

so can I say that this is called 2 dimensional principle component analysis?