Question

I am currently trying to implement eigenfaces with numpy, but it seems to struggle with my 32bit Linux system (I use 32bit because of the formerly bad support for flash and java in 64bit, my processor is 64bit…), because when trying to multiply two vectors to get a matrix (vector * transposed vector) numpy gives me

ValueError: broadcast dimensions too large.

I read that this is due to too little memory and could be solved with 64bit. Is there some way to circumvent this? The matrix would be 528000*528000 elements. According to my paper this big matrix is needed for the covariance matrix (suming up all these huge matrices and then dividing it by the number of matrices).

My piece of code looks like this (I do not understand why numpy gives me a matrix anyway, because for my matrix knowledge it looks the wrong way round (horizontal*vertical), but it worked with examples of smaller size):

tmp = []
for face in faces: # just an array of all face vectors (len = 528000)
    diff = np.subtract(averageFace, face)
    diff = np.asmatrix(diff)
    tmp.append(np.multiply(diff, np.transpose(diff)))
C = np.divide(np.sum(tmp, axis=0), len(tmp))

Answer 1

As pv already elaborated, it’s not really practically feasible to try to produce such huge covariance matrix.

But please note that eigenvectors (explained in your drexel link) of phi* phi^T and phi^T* phi are related and this is the key to make the problem more manageable. See more on this topic in Eigenface.