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Model-based regression clustering for high-dimensional data: application to functional data

  • Emilie DevijverEmail author
Regular Article

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 predictors and high-dimensional response and propose two procedures to cluster observations according to the link between predictors and the response. To reduce the dimension, we propose to use the Lasso estimator, which takes into account the sparsity and a maximum likelihood estimator penalized by the rank, to take into account the matrix structure. To choose the number of components and the sparsity level, we construct a collection of models, varying those two parameters and we select a model among this collection with a non-asymptotic criterion. We extend these procedures to functional data, where predictors and responses are functions. For this purpose, we use a wavelet-based approach. For each situation, we provide algorithms and apply and evaluate our methods both on simulated and real datasets, to understand how they work in practice.

Keywords

Model-based clustering Regression High-dimension  Functional data 

Mathematics Subject Classification

62H30 

Notes

Acknowledgments

I am indebted to Jean-Michel Poggi and Pascal Massart for suggesting me to study this problem, and for stimulating discussions. I am also grateful to Jean-Michel Poggi for carefully reading the manuscript and making many useful suggestions. I thank Yves Misiti and Benjamin Auder for their help to speed up the code. I also thank referees for very interesting improvements and suggestions, and editors for their help for writing this paper. I am also grateful to Irène Gijbels for carefully proofreading the manuscript.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Inria Select, Université Paris SudOrsay CedexFrance

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