Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

SFB649DP2017 024

Spatial Functional Principal Component Analysis with Applications to
Brain Image Data

Yingxing Li
Chen Huang
Wolfgang K. Härdle

This paper considers a fast and effective algorithm for conducting functional principle 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 huge dimensional covariance operator. 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 on the analysis of brain image data. Our extracted factors provide excellent recovery of the risk related regions of interests in human brain and the estimated loadings are very informative in revealing the individual risk attitude.

Principal Component Analysis, Penalized Smoothing, Asymptotics, functional Magnetic Resonance Imaging (fMRI)

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