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A kernel-based classifier on a Riemannian manifold

Author

Listed:
  • Loubes Jean-Michel
  • Pelletier Bruno

    (Université Montpellier II, CC 051, Institut de Mathématiques et de Modélisation de Mo, Montellier Cedex 5, Frankreich)

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.

Suggested Citation

  • Loubes Jean-Michel & Pelletier Bruno, 2008. "A kernel-based classifier on a Riemannian manifold," Statistics & Risk Modeling, De Gruyter, vol. 26(1), pages 35-51, March.
    • Handle: RePEc:bpj:strimo:v:26:y:2008:i:1:p:35-51:n:4
    DOI: 10.1524/stnd.2008.0911
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    References listed on IDEAS

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    1. Pelletier, Bruno, 2005. "Kernel density estimation on Riemannian manifolds," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 297-304, July.
    2. Hendriks, H. & Janssen, J. H. M. & Ruymgaart, F. H., 1993. "Strong uniform convergence of density estimators on compact Euclidean manifolds," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 305-311, March.
    3. El Khattabi, Sana & Streit, Franz, 1996. "Identification analysis in directional statistics," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 45-63, November.
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