[Numpy-discussion] confusion about eigenvector

Arnar Flatberg arnar.flatberg@gmail....
Mon Mar 3 11:42:32 CST 2008

>  i read in some document on the topic of eigenfaces that
>  'Multiplying the sorted eigenvector with  face vector results in
>  getting the
>  face-space vector'
>  facespace=sortedeigenvectorsmatrix *  adjustedfacematrix
>  (when these are numpy.matrices )
This will not work with numpy matrices.* is elementwise mult.

>  that is why the confusion about transposing X inside
> facespace=dot(X.T,u[:,reorder])
>  if  i make matrices out of  sortedeigenvectors, adjustedfacematrix
>  then
>  i will get facespace =sortedeigenvectorsmatrix *  adjustedfacematrix
>  which has a different set of elements than that obtained by
>  dot(X.T, u[:,reorder]).

No, they are the same. u[:, reorder] *is* the sortedeigenvectormatrix,
and the transpose of a matrixproduct: (A*B).T == B.T*A, so your
facespace is just the transpose of mine.

I dont know why you are getting the end result wrong. Perhaps you are
reshaping wrong?

I'll try a complete example :-)
Get example data:

import scipy as sp
from matplotlib.pyplot import *
fn = "frey_rawface.mat"
data = sp.asarray(sp.io.loadmat(fn)['ff'], dtype='d').T

data = data - data.mean(0)
u, s, vt  = sp.linalg.svd(data, 0)

# plot the first 6 eigenimages
for i in range(6):
    subplot(2,3,i+1), imshow(vt[i].reshape((28,20)), cmap=cm.gray)
    axis('image'), xticks([]), yticks([])
title("First 6 eigenfaces")


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