Mode-Based Classifier: A Robust and Flexible Discriminant Analysis for High-Dimensional Data

Abstract

High-dimensional classification is both challenging and of interest in numerous applications. Componentwise distance-based classifiers, which utilize partial information with known categories, such as mean, median and quantiles, provide a convenient way. However, when the input features are heavy-tailed or contain outliers, performance of the centroid classifier can be poor. Beyond that, it frequently occurs that a population consists of two or more subpopulations, the mean, median and quantiles in this scenario fail to capture such a structure that can be instead preserved by mode, which is an appealing measure of considerable significance but might be neglected. This paper thus introduces and investigates componentwise mode-based classifiers that can reveal important structures missed by existing distance-based classifiers. We explore several strategies for defining the family of mode-based classifiers, including the unimodal classifiers, the multimodal classifier and the quantilemode classifier. The unimodal classifiers are proposed based on componentwise unimodal distance and kernel mode estimation, and the multimodal classifier is constructed by identifying all the local modes of a distribution according to a novel introduced algorithm. We establish the asymptotic properties of these methods and demonstrate through simulation studies and three real datasets that the mode-based classifiers compare favorably to the current state-of-art methods.