Near-perfect clustering and classification of second-order stochastic processes

A. Suárez, J. L. Torrecilla, C. Ramos-Carreño, J. R. Berrendero, A. Muñoz-Perera

In this work, conditions are identified under which, in the population limit, perfect separation of functional data can be achieved when the observations are realizations of different second-order stochastic processes. The analysis leverages the geometry induced within each group by the limiting form of a sequence of approximations of the inner product in the reproducing kernel Hilbert space associated to the corresponding covariance function. In regard to this limiting form of the inner product, the functions within that group have unit norm and are mutually orthogonal. Therefore, they are located at the vertices of a regular simplex inscribed in an infinite-dimensional unit sphere. Under fairly general conditions, functions from other groups exhibit norms different from 1, enabling their identification. The effectiveness of the proposed approach is demonstrated in functional clustering and classification problems using both simulated and real-world data.

Keywords: Second-order stochastic processes, near-perfect discrimination, RKHS,

Functional data analysis I
June 10, 2025  11:30 AM
MR 1

N. Acar Denizli, P. Delicado

L. González de la Fuente, A. Nieto Reyes, P. N. Terán Agraz

E. Jerez López, J. R. Berrendero Díaz, J. L. Torrecilla Noguerales