Modal clustering of matrix-variate data

TL;DR

This paper extends modal clustering to matrix-variate data using kernel density estimators and a generalized mean-shift algorithm, addressing high dimensionality and demonstrating effectiveness through simulations and real data applications.

Contribution

It introduces nonparametric matrix-variate density estimators and a generalized mean-shift method for modal clustering in high-dimensional settings.

Findings

Effective clustering in high-dimensional matrix data

Good performance compared to competitors in simulations

Successful application to real high-dimensional datasets

Abstract

The nonparametric formulation of density-based clustering, known as modal clustering, draws a correspondence between groups and the attraction domains of the modes of the density function underlying the data. Its probabilistic foundation allows for a natural, yet not trivial, generalization of the approach to the matrix-valued setting, increasingly widespread, for example, in longitudinal and multivariate spatio-temporal studies. In this work we introduce nonparametric estimators of matrix-variate distributions based on kernel methods, and analyze their asymptotic properties. Additionally, we propose a generalization of the mean-shift procedure for the identification of the modes of the estimated density. Given the intrinsic high dimensionality of matrix-variate data, we discuss some locally adaptive solutions to handle the problem. We test the procedure via extensive simulations, also with respect to some competitors, and illustrate its performance through two high-dimensional real data applications.