A kernel between sets of vectors

In various application domains, including im-age recognition, it is natural to represent each example as a set of vectors. With a base kernel we can implicitly map these vec-tors to a Hilbert space and ¯t a Gaussian distribution to the whole set using Kernel PCA. We de¯ne our kernel between exam-ples as Bhattacharyya's measure of a±nity between such Gaussians. The resulting ker-nel is computable in closed form and enjoys many favorable properties, including graceful behavior under transformations, potentially justifying the vector set representation even in cases when more conventional representa-tions also exist. 1.