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 highdimensional feature spaces. We demonstrate the usage of the matrix-based kernel function f(A B) with experiments on two visual tasks. The first task is the discrimination of "irregular" motion trajectory of an individual or a group of individuals in a video sequence. We use the SVM approach using f(A B) where an input matrix represents the motion trajectory of a group of individuals over a certain (fixed) time frame. We show that the classification (irregular versus regular) greatly outperforms the conventional represent...

• Type: Conference
• Year: 2003
• Where: CVPR
• Authors: Lior Wolf, Amnon Shashua
• Keywords: Computer Vision, CVPR 2003, F(a B, Input Video Sequences, Matrix-based Kernel Function, Motion Trajectory, Original Column Vectors