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Spatial functional principal component analysis with applications to brain image data

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  • Li, Yingxing
  • Huang, Chen
  • Härdle, Wolfgang K.

Abstract

This paper considers a fast and effective algorithm for conducting functional principal component analysis with multivariate factors. Compared with the univariate case, our approach could be more powerful in revealing spatial connections or extracting important features in images. To facilitate fast computation, we connect singular value decomposition with penalized smoothing and avoid estimating a covariance operator in very high dimension. Under regularity assumptions, the results indicate that we may enjoy the optimal convergence rate by employing the smoothness assumption inherent to functional objects. We apply our method to the analysis of brain image data. Our extracted factors provide excellent recovery of the risk related regions of interest in the human brain and the estimated loadings are very informative in revealing individual risk attitude.

Suggested Citation

  • Li, Yingxing & Huang, Chen & Härdle, Wolfgang K., 2019. "Spatial functional principal component analysis with applications to brain image data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 263-274.
    • Handle: RePEc:eee:jmvana:v:170:y:2019:i:c:p:263-274
    DOI: 10.1016/j.jmva.2018.11.004
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    Cited by:

    1. Michael Greenacre & Patrick J. F Groenen & Trevor Hastie & Alfonso Iodice d’Enza & Angelos Markos & Elena Tuzhilina, 2023. "Principal component analysis," Economics Working Papers 1856, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.

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