[Numpy-discussion] confusion about eigenvector

[Matthieu Brucher]

Hi,

If your images are 4x3, your eigenvector must be 12 long.

Matthieu

2008/2/28, devnew at gmail.com <devnew at gmail.com>:
>
> 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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-- 
French PhD student
Website : http://matthieu-brucher.developpez.com/
Blogs : http://matt.eifelle.com and http://blog.developpez.com/?blog=92
LinkedIn : http://www.linkedin.com/in/matthieubrucher
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