Bayesian Model Selection Methods for Mutual and Symmetric $k$-Nearest Neighbor Classification
This work addresses classification accuracy issues for users of nearest neighbor methods, but it is incremental as it builds on existing variants with Bayesian enhancements.
The authors tackled the problem of improving k-nearest neighbor classification by proposing Bayesian model selection methods for mutual and symmetric variants, resulting in performance that is better than or comparable to existing methods with cross-validation on both artificial and real-world datasets.
The $k$-nearest neighbor classification method ($k$-NNC) is one of the simplest nonparametric classification methods. The mutual $k$-NN classification method (M$k$NNC) is a variant of $k$-NNC based on mutual neighborship. We propose another variant of $k$-NNC, the symmetric $k$-NN classification method (S$k$NNC) based on both mutual neighborship and one-sided neighborship. The performance 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 be performed based on Bayesian mutual and symmetric $k$-NN regression methods with the selection schemes for the parameter $k$. Bayesian mutual and symmetric $k$-NN regression methods are based on Gaussian process models, and it turns out that they can do M$k$NN and S$k$NN classification with new encodings of target values (class labels). The simulation results show that the proposed methods are better than or comparable to $k$-NNC, M$k$NNC and S$k$NNC with the parameter $k$ selected by the leave-one-out cross validation method not only for an artificial data set but also for real world data sets.