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Clustering multivariate functional data in group-specific functional subspaces

Author

Listed:
  • Amandine Schmutz

    (Lim France
    Ecole Nationale Vétérinaire d’Alfort)

  • Julien Jacques

    (Université de Lyon, Lyon 2)

  • Charles Bouveyron

    (Université Côte d’Azur)

  • Laurence Chèze

    (Université de Lyon, Lyon 1)

  • Pauline Martin

    (Lim France
    Ecole Nationale Vétérinaire d’Alfort)

Abstract

With the emergence of numerical sensors in many aspects of everyday life, there is an increasing need in analyzing multivariate functional data. This work focuses on the clustering of such functional data, in order to ease their modeling and understanding. To this end, a novel clustering technique for multivariate functional data is presented. This method is based on a functional latent mixture model which fits the data into group-specific functional subspaces through a multivariate functional principal component analysis. A family of parsimonious models is obtained by constraining model parameters within and between groups. An Expectation Maximization algorithm is proposed for model inference and the choice of hyper-parameters is addressed through model selection. Numerical experiments on simulated datasets highlight the good performance of the proposed methodology compared to existing works. This algorithm is then applied to the analysis of the pollution in French cities for 1 year.

Suggested Citation

  • Amandine Schmutz & Julien Jacques & Charles Bouveyron & Laurence Chèze & Pauline Martin, 2020. "Clustering multivariate functional data in group-specific functional subspaces," Computational Statistics, Springer, vol. 35(3), pages 1101-1131, September.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:3:d:10.1007_s00180-020-00958-4
    DOI: 10.1007/s00180-020-00958-4
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    Cited by:

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    2. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. Philip A. White & Alan E. Gelfand, 2021. "Multivariate functional data modeling with time-varying clustering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 586-602, September.
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    5. Amovin-Assagba, Martial & Gannaz, Irène & Jacques, Julien, 2022. "Outlier detection in multivariate functional data through a contaminated mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    6. Fang, Kuangnan & Chen, Yuanxing & Ma, Shuangge & Zhang, Qingzhao, 2022. "Biclustering analysis of functionals via penalized fusion," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Rhoden, Imke & Weller, Daniel & Voit, Ann-Katrin, 2021. "Spatio-temporal dynamics of European innovation: An exploratory approach via multivariate functional data cluster analysis," Ruhr Economic Papers 926, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    8. Daewon Yang & Taeryon Choi & Eric Lavigne & Yeonseung Chung, 2022. "Non‐parametric Bayesian covariate‐dependent multivariate functional clustering: An application to time‐series data for multiple air pollutants," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1521-1542, November.

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