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Biometrika 2003 90(1):99-112; doi:10.1093/biomet/90.1.99
© 2003 by Biometrika Trust
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Likelihood inference in nearest-neighbour classification models

Christopher C.Holmes1 and Niall M.Adams1

1 Department of Mathematics, Imperial College, London, SW7 2BZ, U.Kc.holmes{at}ic.ac.uk n.adams{at}ic.ac.uk

Traditionally the neighbourhood size k in the k-nearest-neighbour algorithm is either fixed at the first nearest neighbour or is selected on the basis of a crossvalidation study.In this paper we present an alternative approach that develops the k-nearest-neighbour algorithm using likelihood-based inference. Our method takes the form of a generalised linear regression on a set of k-nearest-neighbour autocovariates. By defining the k-nearest-neighbour algorithm in this way we are able to extend the method to accommodate the original predictor variables as possible linear effects as well as allowing for the inclusion of multiple nearest-neighbour terms. The choice of the final model proceeds via a stepwise regression procedure. It is shown that our method incorporates a conventional generalised linear model and a conventional k-nearest-neighbour algorithm as special cases. Empirical results suggest that the method out-performs the standard k-nearest-neighbour method in terms of misclassification rate on a wide variety of datasets.

Key Words: Maximum pseudolikelihood; k nearest neighbour; Nonparametric classification; Probabilistic nearest neighbour

Received March 2001. Revised December 2001


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