# Principal component analysis basis vectors

I have high dimensional data (known to be similar) which is organized into the columns of matrix Q. I perform a princomp on this data, and project the centered columns of Q onto the calculated eigenvector basis (the first 4).

My question is, can I use the linearly independent vectors of the result A to form a basis for which I can test other high dim data for similarity? e.g. Solve Ax=b for an exact solution? I think the usual way of determining similarity is by Euclidean distance, but I wonder if this is possible too.

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Just to clarify - what do you mean by "known to be similar"? (OT: Interesting username - is it novel or derived from something?) –  Iterator Aug 15 '11 at 1:41
It's definitely possible to compare two datasets, however are you looking for a statistical formulation of a test, or more of a descriptive formulation (e.g. the difference between a t-test and Euclidean distance)? Both are feasible, but are very different questions. –  Iterator Aug 15 '11 at 1:44
The data is comprised of training images that have similar parameters. I would like to get other (test) images that "fit into the group". Thus, the parameters are unknown for the test images and I thought I could use principal component analysis. The username is from the subreddit fifthworldproblems. –  FiFThWoRlDFreaKo Aug 15 '11 at 1:48
Is this question, also on images, similar to yours? stackoverflow.com/questions/7061004/… –  Iterator Aug 15 '11 at 1:50
It's a very different methodology, certainly. –  Iterator Aug 15 '11 at 1:51
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