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 prob- ability of error converges to the Bayes risk with probability one.