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

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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...
Lior Wolf, Amnon Shashua
Added 12 Oct 2009
Updated 12 Oct 2009
Type Conference
Year 2003
Where CVPR
Authors Lior Wolf, Amnon Shashua
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