On the Use of Diagonal and Class-Dependent Weighted Distances for the Probabilistic k-Nearest Neighbor

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 class-dependent 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.