  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.
