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Clustering functional data into groups by using projections

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  • Aurore Delaigle
  • Peter Hall
  • Tung Pham

Abstract

We show that, in the functional data context, by appropriately exploiting the functional nature of the data, it is possible to cluster the observations asymptotically perfectly. We demonstrate that this level of performance can sometimes be achieved by the k‐means algorithm as long as the data are projected on a carefully chosen finite dimensional space. In general, the notion of an ideal cluster is not clearly defined. We derive our results in the setting where the data come from two populations whose distributions differ at least in terms of means, and where an ideal cluster corresponds to one of these two populations. We propose an iterative algorithm to choose the projection functions in a way that optimizes clustering performance, where, to avoid peculiar solutions, we use a weighted least squares criterion. We apply our iterative clustering procedure on simulated and real data, where we show that it works well.

Suggested Citation

  • Aurore Delaigle & Peter Hall & Tung Pham, 2019. "Clustering functional data into groups by using projections," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 271-304, April.
  • Handle: RePEc:bla:jorssb:v:81:y:2019:i:2:p:271-304
    DOI: 10.1111/rssb.12310
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Chenlei Leng & Degui Li & Hanlin Shang & Yingcun Xia, 2024. "Covariance Function Estimation for High-Dimensional Functional Time Series with Dual Factor Structures," Papers 2401.05784, arXiv.org, revised Jan 2024.
    2. Qingzhi Zhong & Huazhen Lin & Yi Li, 2021. "Cluster non‐Gaussian functional data," Biometrics, The International Biometric Society, vol. 77(3), pages 852-865, September.
    3. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    5. Li, Ting & Song, Xinyuan & Zhang, Yingying & Zhu, Hongtu & Zhu, Zhongyi, 2021. "Clusterwise functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).

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