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Dimension-Reduced Clustering of Functional Data via Subspace Separation

Author

Listed:
  • Michio Yamamoto

    (Kyoto University Graduate School of Medicine)

  • Heungsun Hwang

    (McGill University)

Abstract

We propose a new method for finding an optimal cluster structure of functions as well as an optimal subspace for clustering simultaneously. The proposed method aims to minimize a distance between functional objects and their projections with the imposition of clustering penalties. It includes existing approaches to functional cluster analysis and dimension reduction, such as functional principal component k-means (Yamamoto, 2012) and functional factorial k-means (Yamamoto and Terada, 2014), as special cases. We show that these existing methods can perform poorly when a disturbing structure exists and that the proposed method can overcome this drawback by using subspace separation. A novel model selection procedure has been proposed, which can also be applied to other joint analyses of dimension reduction and clustering. We apply the proposed method to artificial and real data to demonstrate its performance as compared to the extant approaches.

Suggested Citation

  • Michio Yamamoto & Heungsun Hwang, 2017. "Dimension-Reduced Clustering of Functional Data via Subspace Separation," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 294-326, July.
    • Handle: RePEc:spr:jclass:v:34:y:2017:i:2:d:10.1007_s00357-017-9232-z
    DOI: 10.1007/s00357-017-9232-z
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Virta, Joni & Li, Bing & Nordhausen, Klaus & Oja, Hannu, 2020. "Independent component analysis for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    3. Weikuan Jia & Dean Zhao & Ling Ding & Yuanjie Zheng, 2019. "A Reliable Small Sample Classification Algorithm by Elman Neural Network Based on PLS and GA," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 306-321, July.
    4. Matthieu Marbac & Mohammed Sedki & Tienne Patin, 2020. "Variable Selection for Mixed Data Clustering: Application in Human Population Genomics," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 124-142, April.

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