Institute of Statistical Science, Academia Sinica & International Chinese Statistical Association
Doi
Abstract
This file available on this institutional repository is a preprint. It has not been certified by peer review. It is freely available at http://www3.stat.sinica.edu.tw/ss_newpaper/SS-2023-0014_na.pdf.Supplementary Materials: In the supplementary materials, we present additional results for simulation examples and real data analysis, and provide the technical results of Theorems 1-3.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.The research of W. Xiong was supported in part by NSFC grants 12001101 and the Fundamental Research
Funds for the Central Universities in UIBE CXTD14-05