PCA implicitly uses a quadratic form on a vector space. When done the usual way, this is just the identity matrix. But for image data, I think you would get b

PCA implicitly uses a quadratic form on a vector space. When done the usual way, this is just the identity matrix. But for image data, I think you would get better results using a quadratic form based on a kernel, so that Q_ijkl where (i,j) and (k,l) are pixel coordinates, is given by Q_ijkl = t((i-k)^2 + (j,l)^2) for some kernel function t.