Kernel Principal Angles for Classification Machines with Applications to Image Sequence Interpretation

We consider the problem of learning with instances defined over a space of sets of vectors. We derive a new positive definite kernel f(A,B) defined over pairs of matrices A,B based on the concept of principal angles between two linear subspaces. We show that the principal angles can be recovered using only inner-products between pairs of column vectors of the input matrices thereby allowing the original column vectors of A,B to be mapped onto arbitrarily high-dimensional feature spaces. We apply this technique to inference over image sequences applications of face recognition and irregular motion trajectory detection.