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I'm not sure this is the right place but here I go:

I have a database of 300 picture in high-resolution. I want to compute the PCA on this database and so far here is what I do: - reshape every image as a single column vector - create a matrix of all my data (500x300) - compute the average column and substract it to my matrix, this gives me X - compute the correlation C = X'*X (300x300) - find the eigenvectors V and Eigen Values D of C. - the PCA matrix is given by X*V*D^-1/2, where each column is a Principal Component

This is great and gives me correct component.

Now what I'm doing is doing the same PCA on the same database, except that the images have a lower resolution.

http://i.imgur.com/f18sB.png

Here are my results, low-res on the left and high-res on the right. Has you can see most of them are similar but SOME images are not the same (the ones I circled)

Is there any way to explain this? I need for my algorithm to have the same images, but one set in high-res and the other one in low-res, how can I make this happen?

thanks

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1 Answer 1

up vote 1 down vote accepted

The basis vectors produced by PCA won't necessarily be in the same order after downsampling the training set, because high-frequency features won't be considered. If you need a 1:1 mapping, downsample the basis vectors themselves, rather than the training set. The resultant basis vectors won't be ordered by importance anymore, but that may not matter to you.

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