A kernel-based classifier on a Riemannian manifold

Abstract

Let X be a random variable taking values in a compact Riemannian manifold without boundary, and let Y be a discrete random variable valued in {0;1} which represents a classification label. We introduce a kernel rule for classification on the manifold based on n independent copies of ( X , Y ). Under mild assumptions on the bandwidth sequence, it is shown that this kernel rule is consistent in the sense that its probability of error converges to the Bayes risk with probability one.