Spatial functional principal component analysis with applications to brain image data

摘要

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. (C) 2018 Elsevier Inc. All rights reserved.