On the use of diagonal and class-dependent weighted distances for the probabilistic k-nearest neighbor

Authors:
Roberto Paredes;Mark Girolami
Affiliations:
Instituto Tecnológico de Informática, Universidad Politécnica de Valencia, Valencia, Spain;University of Glasgow, UK
Venue:
IbPRIA'11 Proceedings of the 5th Iberian conference on Pattern recognition and image analysis
Year:
2011

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Abstract

A probabilistic k-nn (PKnn) method was introduced in [13] under the Bayesian point of view. This work showed that posterior inference over the parameter k can be performed in a relatively straightforward manner using Markov Chain Monte Carlo (MCMC) methods. This method was extended by Everson and Fieldsen [14] to deal with metric learning. In this work we propose two different dissimilarities functions to be used inside this PKnn framework. These dissimilarities functions can be seen as a simplified version of the full-covariance distance functions just proposed. Furthermore we propose to use a classdependent dissimilarity function as proposed in [8] aim at improving the k-nn classifier. In the present work we pursue a simultaneously learning of the dissimilarity function parameters together with the parameter k of the k-nn classifier. The experiments show that this simultaneous learning lead to an improvement of the classifier with respect to the standard k-nn and state-of-the-art technique as well.