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Classification methods for Hilbert data based on surrogate density

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  • Bongiorno, Enea G.
  • Goia, Aldo

Abstract

An unsupervised and a supervised classification approach 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.

Suggested Citation

  • Bongiorno, Enea G. & Goia, Aldo, 2016. "Classification methods for Hilbert data based on surrogate density," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 204-222.
    • Handle: RePEc:eee:csdana:v:99:y:2016:i:c:p:204-222
    DOI: 10.1016/j.csda.2016.01.019
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    Cited by:

    1. Adriano Zanin Zambom & Julian A. A. Collazos & Ronaldo Dias, 2019. "Functional data clustering via hypothesis testing k-means," Computational Statistics, Springer, vol. 34(2), pages 527-549, June.
    2. 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.
    3. Simon Nanty & Céline Helbert & Amandine Marrel & Nadia Pérot & Clémentine Prieur, 2017. "Uncertainty quantification for functional dependent random variables," Computational Statistics, Springer, vol. 32(2), pages 559-583, June.
    4. Daniel Kosiorowski & Jerzy P. Rydlewski, 2020. "Centrality-oriented causality. A study of EU agricultural subsidies and digital developement in Poland," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(3), pages 47-63.
    5. Aubin, Jean-Baptiste & Bongiorno, Enea G. & Goia, Aldo, 2022. "The correction term in a small-ball probability factorization for random curves," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    6. Zhang, Yi-Chen & Sakhanenko, Lyudmila, 2019. "The naive Bayes classifier for functional data," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 137-146.
    7. Kosiorowski Daniel & Jerzy P. Rydlewski, 2019. "Centrality-oriented Causality -- A Study of EU Agricultural Subsidies and Digital Developement in Poland," Papers 1908.11099, arXiv.org, revised Sep 2019.
    8. 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.
    9. Enea G. Bongiorno & Aldo Goia & Philippe Vieu, 2019. "Modeling functional data: a test procedure," Computational Statistics, Springer, vol. 34(2), pages 451-468, June.

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