Model-based regression clustering for high-dimensional data. Application to functional data

TL;DR

This paper introduces novel model-based regression clustering methods tailored for high-dimensional and functional data, utilizing sparsity and matrix structure penalties, with demonstrated effectiveness on simulations and real-world datasets.

Contribution

It develops two procedures combining Lasso and rank penalties for high-dimensional regression, extended to functional data via wavelet methods, with algorithms and empirical evaluation.

Findings

Effective handling of high-dimensional predictors and responses.

Successful application to functional data using wavelet-based approach.

Validated methods through simulations and real data analysis.

Abstract

Finite mixture regression models are useful for modeling the relationship between response and predictors, arising from different subpopulations. In this article, we study high-dimensional predic- tors and high-dimensional response, and propose two procedures to deal with this issue. We propose to use the Lasso estimator to take into account the sparsity, and a penalty on the rank, to take into account the matrix structure. Then, we extend these procedures to the functional case, where predictors and responses are functions. For this purpose, we use a wavelet-based approach. Finally, for each situation, we provide algorithms, and apply and evaluate our methods both on simulations and real datasets.