Classification methods for Hilbert data based on surrogate density

TL;DR

This paper introduces new classification methods for Hilbert data using surrogate density estimates based on principal components, demonstrating their effectiveness through simulations and real data applications.

Contribution

It proposes novel unsupervised and supervised classification algorithms for Hilbert data utilizing a surrogate density derived from small-ball probabilities and kernel estimation.

Findings

Effective classification on simulated datasets

Successful application to real datasets

Insights into parameter tuning and computational aspects

Abstract

An unsupervised and a supervised classification approaches for Hilbert random curves are studied. Both rest on the use of a surrogate of the probability density which is defined, in a distribution-free mixture context, from an asymptotic factorization of the small-ball probability. That surrogate density is estimated by a kernel approach from the principal components of the data. The focus is on the illustration of the classification algorithms and the computational implications, with particular attention to the tuning of the parameters involved. Some asymptotic results are sketched. Applications on simulated and real datasets show how the proposed methods work.