On Sat, Mar 1, 2008 at 8:27 AM, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote: > > > This example assumes that facearray is an ndarray.(like you described > > in original post ;-) ) 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? Yes, you may > why do i need to get the transpose? You dont need to. I did because then it would put the eigenvectors that span your column space as columns of the facespace array. I figured that would be easier for you, as that would be compatible with the use of eig (eigh) and matlab > then i can take as eigface_image0= vt[0].reshape(imgwdth,imght) > > 2.this way (svd) is diff from covariance matrix method. No it is not. You may be fooled by the scaling though. I see from the post above, that there may be some confusion here about svd and eig on a crossproduct matrix :-) 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 _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
