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A probabilistic nearest neighbour method for statistical pattern recognition

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  • C. C. Holmes
  • N. M. Adams

Abstract

Summary. Nearest neighbour algorithms are among the most popular methods used in statistical pattern recognition. The models are conceptually simple and empirical studies have shown that their performance is highly competitive against other techniques. However, the lack of a formal framework for choosing the size of the neighbourhood k is problematic. Furthermore, the method can only make discrete predictions by reporting the relative frequency of the classes in the neighbourhood of the prediction point. We present a probabilistic framework for the k‐nearest‐neighbour method that largely overcomes these difficulties. Uncertainty is accommodated via a prior distribution on k as well as in the strength of the interaction between neighbours. These prior distributions propagate uncertainty through to proper probabilistic predictions that have continuous support on (0, 1). The method makes no assumptions about the distribution of the predictor variables. The method is also fully automatic with no user‐set parameters and empirically it proves to be highly accurate on many bench‐mark data sets.

Suggested Citation

  • C. C. Holmes & N. M. Adams, 2002. "A probabilistic nearest neighbour method for statistical pattern recognition," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 295-306, May.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:2:p:295-306
    DOI: 10.1111/1467-9868.00338
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    References listed on IDEAS

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    1. D. J. Hand & W. E. Henley, 1997. "Statistical Classification Methods in Consumer Credit Scoring: a Review," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 160(3), pages 523-541, September.
    2. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
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    Cited by:

    1. Ghosh, Annesha & Ghosh, Anil K. & SahaRay, Rita & Sarkar, Soham, 2025. "Classification using global and local Mahalanobis distances," Journal of Multivariate Analysis, Elsevier, vol. 207(C).
    2. Ghosh, Anil K., 2006. "On optimum choice of k in nearest neighbor classification," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3113-3123, July.
    3. Ha-Thu Nguyen, 2015. "How is credit scoring used to predict default in China?," EconomiX Working Papers 2015-1, University of Paris Nanterre, EconomiX.
    4. Giuseppe Nuti, 2019. "An Efficient Algorithm for Bayesian Nearest Neighbours," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1251-1258, December.
    5. Ha Thu Nguyen, 2015. "How is credit scoring used to predict default in China?," Working Papers hal-04133309, HAL.
    6. Subhajit Dutta & Anil K. Ghosh, 2017. "Discussion," International Statistical Review, International Statistical Institute, vol. 85(1), pages 40-43, April.
    7. Pya Arnqvist, Natalya & Ngendangenzwa, Blaise & Lindahl, Eric & Nilsson, Leif & Yu, Jun, 2021. "Efficient surface finish defect detection using reduced rank spline smoothers and probabilistic classifiers," Econometrics and Statistics, Elsevier, vol. 18(C), pages 89-105.
    8. Yinglei Lai & Baolin Wu & Hongyu Zhao, 2011. "A permutation test approach to the choice of size k for the nearest neighbors classifier," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2289-2302.
    9. Mukhopadhyay, Subhadeep & Ghosh, Anil K., 2011. "Bayesian multiscale smoothing in supervised and semi-supervised kernel discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2344-2353, July.
    10. Manahov, Viktor & Hudson, Robert & Gebka, Bartosz, 2014. "Does high frequency trading affect technical analysis and market efficiency? And if so, how?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 28(C), pages 131-157.
    11. Jing Quan & Xuelian Sun, 2024. "Credit risk assessment using the factorization machine model with feature interactions," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 11(1), pages 1-10, December.
    12. Francesco CHELLI & Chiara GIGLIARANO & Elvio MATTIOLI, 2009. "The Impact of Inflation on Heterogeneous Groups of Households: an Application to Italy," Working Papers 329, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.

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