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Article Dans Une Revue Statistics and Decisions Année : 2008

A kernel based classifier on a Riemannian manifold

Résumé

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.
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Dates et versions

hal-00460629 , version 1 (01-03-2010)

Identifiants

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Jean-Michel Loubes, Bruno Pelletier. A kernel based classifier on a Riemannian manifold. Statistics and Decisions, 2008, 26 (1), pp.35-51. ⟨10.1524/stnd.2008.0911⟩. ⟨hal-00460629⟩
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