Smooth Principal Component Analysis with Application to Functional Magnetic Resonance Imaging

Multivariate methods such as principal component analysis (PCA) and independent component analysis (ICA) have been found to be useful in functional magnetic resonance imaging (fMRI) research. They are often able to decompose the fMRI data so that the researcher can associate their components to some biological processes of interest such as the brain response resulting from a stimulus. In this paper we develop a new smooth version of the PCA derived from a maximum likelihood framework. We are thus led to an unusual use of AIC, BIC namely to choose two (rather than one) parameters simultaneously; the number of principal components and the degree of smoothness. The algorithm is applied to real fMRI data