A kernel based classifier on a Riemannian manifold

Jean-Michel Loubes (1) , Bruno Pelletier (2, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Mots clés: Classification; Kernel rule; Bayes risk; Consistency

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

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⟩