This paper presents a general family of algebraic positive definite similarity functions over spaces of matrices with varying column rank. The columns can represent local regions in an image (whereby images have varying number of local parts), images of an image sequence, motion trajectories in a multibody motion, and so forth. The family of set kernels we derive is based on a group invariant tensor product lifting with parameters that can be naturally tuned to provide a cook-book of sorts covering the possible "wish lists" from similarity measures over sets of varying cardinality. We highlight the strengths of our approach by demonstrating the set kernels for visual recognition of pedestrians using local parts representations.
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