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Biometrika 1998 85(4):823-833; doi:10.1093/biomet/85.4.823
© 1998 by Biometrika Trust
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Classification via kernel product estimators

CRAIG A. COOLEY * and STEVEN N. MACEACHERN

Department of Statistics, The Ohio State University 141 Cockins Hall, 1958 Neil Avenue, Columbus, Ohio 43210, U.S.A.snm{at}stat.ohio-state.edu

Multivariate kernel density estimation is often used as the basis for a nonparametric classification technique. However, the multivariate kernel classifier suffers from the curse of dimensionality, requiring inordinately large sample sizes to achieve a reasonable degree of accuracy in high dimensional settings. A variance stabilising approach to kernel classification can be motivated through an alternative interpretation of linear and quadratic discriminant analysis in which rotations of the coordinate axes are employed to obtain an assumed mutual independence among the components of the rotated data. This alternative method, which we call the method of kernel product estimators, performs well in a variety of examples, including a 20-dimensional target recognition problem.

Key Words: Bias-variance trade-off • Density estimation • Discriminant analysis • Nonparametric classification


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