Abstract
k-nearest neighbour (k-nn) model is a simple, popular classifier. Probabilistic k-nn is a more powerful variant in which the model is cast in a Bayesian framework using (reversible jump) Markov chain Monte Carlo methods to average out the uncertainy over the model parameters.
The k-nn classifier depends crucially on the metric used to determine distances between data points. However, scalings between features, and indeed whether some subset of features is redundant, are seldom known a priori. Here we introduce a variable metric extension to the probabilistic k-nn classifier, which permits averaging over all rotations and scalings of the data. In addition, the method permits automatic rejection of irrelevant features. Examples are provided on synthetic data, illustrating how the method can deform feature space and select salient features, and also on real-world data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cover, T., Hart, P.: Nearest neighbor pattern classification. IEEE Transactions on Information Theory 13, 21–27 (1967)
Holmes, C., Adams, N.: A probabilistic nearest neighbour method for statistical pattern recognition. Journal Royal Statistical Society B 64, 1–12 (2002), See also code at http://www.stats.ma.ic.ac.uk/~ccholmes/Book_code/book_code.html
Fan, J., Gijbels, I.: Local polynomial modelling and its applications. Chapman & Hall, London (1996)
Green, P.: Reversible jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrika 82 (1995)
Denison, D., Holmes, C., Mallick, B., Smith, A.: Bayesian Methods for Nonlinear Classification and Regression. Wiley, Chichester (2002)
Larget, B., Simon, D.: Markov Chain Monte Carlo Algorithms for the Bayesian analysis of phylogenetic trees. Molecular Biology and Evolution 16, 750–759 (1999)
Blake, C., Merz, C.: UCI repository of machine learning databases (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html
Sykacek, P.: On input selection with reversible jump Markov chain Monte Carlo sampling. In: Solla, S., Leen, T., Müller, K.R. (eds.) NIPS* 12, pp. 638–644 (2000)
Myles, J.P., Hand, D.J.: The multi-class metric problem in nearest neighbour discrimination rules. Pattern Recognition 23, 1291–1297 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Everson, R.M., Fieldsend, J.E. (2004). A Variable Metric Probabilistic k-Nearest-Neighbours Classifier. In: Yang, Z.R., Yin, H., Everson, R.M. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2004. IDEAL 2004. Lecture Notes in Computer Science, vol 3177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28651-6_96
Download citation
DOI: https://doi.org/10.1007/978-3-540-28651-6_96
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22881-3
Online ISBN: 978-3-540-28651-6
eBook Packages: Springer Book Archive