[Numpy-discussion] confusion about eigenvector
devnew@gmai...
devnew@gmai...
Thu Feb 28 01:17:15 CST 2008
i all
I am learning PCA method by reading up Turk&Petland papers etc
while trying out PCA on a set of greyscale images using python, and
numpy I tried to create eigenvectors and facespace.
i have
facesarray--- an NXP numpy.ndarray that contains data of images
N=numof images,P=pixels in an image
avgarray --1XP array containing avg value for each pixel
adjustedfaces=facesarray-avgarray
adjustedmatrix=matrix(adjustedfaces)
adjustedmatrix_trans=adjustedmatrix.transpose()
covariancematrix =adjustedmatrix*adjustedmatrix_trans
evalues,evect=eigh(covariancematrix)
after sorting such that most significant eigenvectors are selected.
evectmatrix is now my eigenvectors matrix
here is a sample using 4X3 greyscale images
evalues
[ -1.85852801e-13 6.31143639e+02 3.31182765e+03 5.29077871e+03]
evect
[[ 0.5 -0.06727772 0.6496399 -0.56871936]
[ 0.5 -0.77317718 -0.37697426 0.10043632]
[ 0.5 0.27108233 0.31014514 0.76179023]
[ 0.5 0.56937257 -0.58281078 -0.29350719]]
evectmatrix (sorted according to largest evalue first)
[[-0.56871936 0.6496399 -0.06727772 0.5 ]
[ 0.10043632 -0.37697426 -0.77317718 0.5 ]
[ 0.76179023 0.31014514 0.27108233 0.5 ]
[-0.29350719 -0.58281078 0.56937257 0.5 ]]
then i can create facespace by
facespace=evectmat*adjustedfaces
till now i 've been following the steps as mentioned in the PCA
tutorial(by Lindsay smith & others)
what i want to know is that in the above evectmatrix is each row
([-0.56871936 0.6496399 -0.06727772 0.5 ] etc) an eigenvector?
or does a column in the above matrix represent an eigenvector?
to put it differently,
should i represent an eigenvector by
evectmatrix[i] or by
(get_column_i_of(evectmatrix)).transpose()
if someone can make this clear please do
D
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