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I have managed to find the orthogonal basis vectors using PCA (even an idiot like me can plug values into a function). But now I face the problem of my limited experience with data analysis. I have two questions:

• The basis vectors that the pcabuildbasis method returns is equal in dimension to the original data set, I assume that one chooses the top ones that maximise variance?
• Armed with these basis vectors representing a space of reduced dimension, how do I project the original data onto this lower dimensional space? All projections I am familiar with are between spaces of equal dimension.

Can anyone help me?

Thanks in advance for any help!!

OK, I think I might have this myself actually, and it is really simple.

Say you have a point X which is of dimension n, and m < n basis vectors that are the columns of a matrix m x n matrix B = {C1, C2, ... Cm}. To project X onto B you simply calculate transpose(X) x B.

Am I right?

Yes, you are right, but only when C1...Cm are orthonormal (mutually orthogonal and have unit length). Luckily, pcabuildbasis() returns orthogonal matrix :) however, if you try to use some other matrix, it should be orthonormalized before projection.

Could you give the example using code, please?
I am not that good in statistic and I am also not familiar with alglib so it doesn't actually hits as obvious to me.

In addition, I am using this PCA with alglib as an alternative to g77alscal when I am porting an application.
Could anyone clarify that I am on the right track?

Thanks.