1 Mar 2008 06:41
Re: PCA on set of face images
devnew <at> gmail.com <devnew <at> gmail.com>
2008-03-01 05:41:30 GMT
2008-03-01 05:41:30 GMT
On Mar 1, 12:57 am, "Peter Skomoroch" wrote: I think > > matlab example should be easy to translate to scipy/matplotlib using the > > montage function: > > > load faces.mat > > %Form covariance matrix > > C=cov(faces'); > > %build eigenvectors and eigenvalues > > [E,D] = eig(C); hi Peter, nice code..ran the examples.. however couldn't follow the matlab code since i have no exposure to matlab..was using numpy etc for calcs could you confirm the layout for the face images data? i assumed that the initial face matrix should be faces=a numpy matrix with N rows ie N=numofimages row1=image1pixels as a sequence row2=image2pixels as a sequence ... rowN=imageNpixels as a sequence and covariancematrix=faces*faces_transpose is this the right way? thanks(Continue reading)
) It looks like you are using a matrix.
hi Arnar
thanks ..
a few doubts however
1.when i use say 10 images of 4X3 each
u, s, vt = linalg.svd(facearray, 0)
i will get vt of shape (10,12)
can't i take this as facespace? why do i need to get the transpose?
then i can take as eigface_image0= vt[0].reshape(imgwdth,imght)
2.this way (svd) is diff from covariance matrix method. if i am to do
it using the later ,how can i get the eigenface image data?
thanks for the help
D
Essentially, if X is a column centered array of size (num_images, num_pixels):
u, s, vt = linalg.svd(X),
Then, the columns of u span the space of dot(X, X.T), the rows of vt
span the space of dot(X.T, X) and s is a vector of scaling
coefficients. Another way of seeing this is that u spans the column
space of X, and vt spans the row space of X. So, for a third view, the
columns of u are the eigenvectors of dot(X, X.T) and the rows of vt
contains the eigenvectors of dot(X.T, X).
Now, in your, `covariance method` you use eigh(dot(X, X.T)), where the
eigenvectors would be exactly the same as u(the array) from an svd on
X. In order to recover the facespace you use facespace=dot(X.T, u).
This facespace is the same as s*vt.T, where s and vt are from the svd.
In my example, the eigenvectors spanning the column space were scaled.
I called this for scores: (u*s)
In your computation the facespace gets scaled implicit. Where to put
the scale is different from application to application and has no
clear definition.
I dont know if this made anything any clearer. However, a simple
example may be clearer:
-------
# X is (a ndarray, *not* matrix) column centered with vectorized images in rows
# method 1:
XX = dot(X, X.T)
s, u = linalg.eigh(XX)
reorder = s.argsort()[::-1]
facespace = dot(X.T, u[:,reorder])
# method 2:
u, s, vt = svd(X, 0)
facespace2 = s*vt.T
------
This gives identical result.
Please remember that eigenvector signs are arbitrary when comparing.
> if i am to do
> it using the later ,how can i get the eigenface image data?
Just like I described before
Arnar
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