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1 IMT - Institut de Mathématiques de Toulouse UMR5219 2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Keywords : Classification Kernel rule Bayes risk Consistency

Author: Jean-Michel Loubes - Bruno Pelletier -

Source: https://hal.archives-ouvertes.fr/


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