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

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  • Emilie Devijver

    (Inria Select, Université Paris Sud)

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.

Suggested Citation

  • Emilie Devijver, 2017. "Model-based regression clustering for high-dimensional data: application to functional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(2), pages 243-279, June.
    • Handle: RePEc:spr:advdac:v:11:y:2017:i:2:d:10.1007_s11634-016-0242-1
    DOI: 10.1007/s11634-016-0242-1
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    References listed on IDEAS

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    1. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    2. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    3. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    4. Nicolai Meinshausen & Peter Bühlmann, 2010. "Stability selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 417-473, September.
    5. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
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    Cited by:

    1. Shutong Chen & Weijun Xie, 2022. "On Cluster-Aware Supervised Learning: Frameworks, Convergent Algorithms, and Applications," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 481-502, January.
    2. Rodney V. Fonseca & Aluísio Pinheiro, 2020. "Wavelet estimation of the dimensionality of curve time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1175-1204, October.

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