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Clustering functional data sets by law

Author

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  • Galves, Antonio
  • Najman, Fernando A.
  • Svarc, Marcela
  • Vargas, Claudia D.

Abstract

We introduce a new clustering procedure for functional data analysis which can classify independent sets of functional samples by their probabilistic law, i.e. that aims to assign data sets to the same cluster if and only if the data were generated with the same underlying distribution. This method has the virtue of being non-supervised and non-parametric, allowing for exploratory investigation with few assumptions about the data. We also present rigorous finite bounds that give us the effect of the number of samples in each dataset on the classification. We also provide an objective heuristic that consistently selects the best partition in a data-driven manner. We show the performance of the method by clustering simulated datasets generated with different distributions.

Suggested Citation

  • Galves, Antonio & Najman, Fernando A. & Svarc, Marcela & Vargas, Claudia D., 2026. "Clustering functional data sets by law," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002406
    DOI: 10.1016/j.spa.2025.104796
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    References listed on IDEAS

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    1. Yingqiu Zhu & Qiong Deng & Danyang Huang & Bingyi Jing & Bo Zhang, 2021. "Clustering based on Kolmogorov–Smirnov statistic with application to bank card transaction data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 558-578, June.
    2. R'emy Chicheportiche & Jean-Philippe Bouchaud, 2012. "Weighted Kolmogorov-Smirnov test: Accounting for the tails," Papers 1207.7308, arXiv.org, revised Oct 2012.
    3. Fernando A Najman & Antonio Galves & Marcela Svarc & Claudia D Vargas, 2025. "Extracting the fingerprints of sequences of random rhythmic auditory stimuli from electrophysiological data," PLOS Computational Biology, Public Library of Science, vol. 21(1), pages 1-18, January.
    4. Aline Duarte & Ricardo Fraiman & Antonio Galves & Guilherme Ost & Claudia D. Vargas, 2019. "Retrieving a Context Tree from EEG Data," Mathematics, MDPI, vol. 7(5), pages 1-13, May.
    5. Naaman, Michael, 2021. "On the tight constant in the multivariate Dvoretzky–Kiefer–Wolfowitz inequality," Statistics & Probability Letters, Elsevier, vol. 173(C).
    6. Wei, Fan & Dudley, Richard M., 2012. "Two-sample Dvoretzky–Kiefer–Wolfowitz inequalities," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 636-644.
    7. Juan Antonio Cuesta-Albertos & Ricardo Fraiman & Thomas Ransford, 2007. "A Sharp Form of the Cramér–Wold Theorem," Journal of Theoretical Probability, Springer, vol. 20(2), pages 201-209, June.
    8. González–Rodríguez, Gil & Colubi, Ana & González–Manteiga, Wenceslao & Febrero–Bande, Manuel, 2024. "A consistent test of equality of distributions for Hilbert-valued random elements," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
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