Particularly important is the ability to incorporate domain knowledge of invariances, e.g., translational invariance ofimages. Kernels based onthemaximumsimilarity overagroup of transformations are not generally positive definite. Perhaps it is for this reason that they have not been studied theoretically. We address this lacuna and show thatpositivedefiniteness indeed holdswith high probabilityforkernels based on the maximum similarity in the small training sample set regime of interest, and that they do yield the best results in that regime.

Particularly important is the ability to incorporate domain knowledge of invariances, e.g., translational invariance ofimages. Kernels based onthemaximumsimilarity overagroup of transformations are not generally positive definite. Perhaps it is for this reason that they have not been studied theoretically. We address this lacuna and show thatpositivedefiniteness indeed holdswith high probabilityforkernels based on the maximum similarity in the small training sample set regime of interest, and that they do yield the best results in that regime.