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Independent component analysis for multivariate functional data

Author

Listed:
  • Virta, Joni
  • Li, Bing
  • Nordhausen, Klaus
  • Oja, Hannu

Abstract

We extend two methods of independent component analysis, fourth order blind identification and joint approximate diagonalization of eigen-matrices, to vector-valued functional data. Multivariate functional data occur naturally and frequently in modern applications, and extending independent component analysis to this setting allows us to distill important information from this type of data, going a step further than the functional principal component analysis. To allow the inversion of the covariance operator we make the assumption that the dependency between the component functions lies in a finite-dimensional subspace. In this subspace we define fourth cross-cumulant operators and use them to construct the two novel, Fisher consistent methods for solving the independent component problem for vector-valued functions. Both simulations and an application on a hand gesture data set show the usefulness and advantages of the proposed methods over functional principal component analysis.

Suggested Citation

  • Virta, Joni & Li, Bing & Nordhausen, Klaus & Oja, Hannu, 2020. "Independent component analysis for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:jmvana:v:176:y:2020:i:c:s0047259x19300223
    DOI: 10.1016/j.jmva.2019.104568
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    References listed on IDEAS

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    1. Marc Vidal & Mattia Rosso & Ana M. Aguilera, 2021. "Bi-Smoothed Functional Independent Component Analysis for EEG Artifact Removal," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
    2. Klaus Nordhausen & Anne Ruiz-Gazen, 2022. "On the usage of joint diagonalization in multivariate statistics," Post-Print hal-04296111, HAL.
    3. Archimbaud, Aurore & Boulfani, Fériel & Gendre, Xavier & Nordhausen, Klaus & Ruiz-Gazen, Anne & Virta, Joni, 2021. "ICS for multivariate functional anomaly detection with applications to predictive maintenance and quality control," TSE Working Papers 21-1182, Toulouse School of Economics (TSE), revised Mar 2022.
    4. Zhong, Rou & Liu, Shishi & Li, Haocheng & Zhang, Jingxiao, 2022. "Robust functional principal component analysis for non-Gaussian longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Nordhausen, Klaus & Ruiz-Gazen, Anne, 2021. "On the usage of joint diagonalization in multivariate statistics," TSE Working Papers 21-1268, Toulouse School of Economics (TSE).
    6. Nordhausen, Klaus & Ruiz-Gazen, Anne, 2022. "On the usage of joint diagonalization in multivariate statistics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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