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)