In this paper we introduce a simple and intuitive adaptive k nearest neighbours classifier, and explore its utility within the context of bootstrap aggregating ("bagging"). The approach is based on finding discriminant subspaces which are computationally efficient to compute, and are motivated by enhancing the discrimination of classes through nearest neighbour classifiers. This adaptiveness promotes diversity of the individual classifiers fit across different bootstrap samples, and so further leverages the variance reducing effect of bagging. Extensive experimental results are presented documenting the strong performance of the proposed approach in comparison with Random Forest classifiers, as well as other nearest neighbours based ensembles from the literature, plus other relevant benchmarks. Code to implement the proposed approach is available in the form of an R package from https://github.com/DavidHofmeyr/BOPNN.

Abstract--In this paper we formulate a probabilistic model for class-specific discriminant subspace learning. The proposed model can naturally incorporate the multi-modal structure of the negative class, which is neglected by existing methods. Moreover, it can be directly used to define a probabilistic classification rule in the discriminant subspace. We show that existing class-specific discriminant analysis methods are special cases of the proposed probabilistic model and, by casting them as probabilistic models, they can be extended to class-specific classifiers. We illustrate the performance of the proposed model, in comparison with that of related methods, in both verification and classification problems.

We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace containing the component means of a GMM with a common covariance matrix also contains the modes of the density and the class means. This motivates us to find a subspace by applying weighted principal component analysis to the modes of a kernel density and the class means. To circumvent the difficulty of deciding the kernel bandwidth, we acquire multiple subspaces from the kernel densities based on a sequence of bandwidths. The GMM constrained by each subspace is estimated; and the model yielding the maximum likelihood is chosen. A dimension reduction property is proved in the sense of being informative for classification or clustering. Experiments on real and simulated data sets are conducted to examine several ways of determining the subspace and to compare with the reduced rank mixture discriminant analysis (MDA). Our new method with the simple technique of spanning the subspace only by class means often outperforms the reduced rank MDA when the subspace dimension is very low, making it particularly appealing for visualization.