Eigenfaces: PCA tends to find a p-dimensional subspace

whose basis vectors correspond to the maximum

variance direction in the original image space (p  N).

We called the new subspace defined by basis vectors “face

space”. First, all training faces are projected onto the face

space to find a set of weights that describes the contribution

of each vector. Then we project all testing faces onto the

face space to obtain a set of weights. Finally, we identify

the face by comparing a set of weights for the testing face

to sets of weights of training faces.