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The $k$-nearest neighbor classification method ($k$-NNC) is one of thesimplest nonparametric classification methods. The mutual $k$-NN classificationmethod (M$k$NNC) is a variant of $k$-NNC based on mutual neighborship. Wepropose another variant of $k$-NNC, the symmetric $k$-NN classification method(S$k$NNC) based on both mutual neighborship and one-sided neighborship. Theperformance of M$k$NNC and S$k$NNC depends on the parameter $k$ as the one of$k$-NNC does. We propose the ways how M$k$NN and S$k$NN classification can beperformed based on Bayesian mutual and symmetric $k$-NN regression methods withthe selection schemes for the parameter $k$. Bayesian mutual and symmetric$k$-NN regression methods are based on Gaussian process models, and it turnsout that they can do M$k$NN and S$k$NN classification with new encodings oftarget values (class labels). The simulation results show that the proposedmethods are better than or comparable to $k$-NNC, M$k$NNC and S$k$NNC with theparameter $k$ selected by the leave-one-out cross validation method not onlyfor an artificial data set but also for real world data sets.

Bayesian Model Selection Methods for Mutual and Symmetric $k$-Nearest Neighbor Classification