Functional principal component analysis of fMRI data.

We describe a principal component analysis (PCA) method for functional magnetic resonance imaging (fMRI) data based on functional data analysis, an advanced nonparametric approach. The data delivered by the fMRI scans are viewed as continuous functions of time sampled at the interscan interval and subject to observational noise, and are used accordingly to estimate an image in which smooth functions replace the voxels. The techniques of functional data analysis are used to carry out PCA directly on these functions. We show that functional PCA is more effective than is its ordinary counterpart in recovering the signal of interest, even if limited or no prior knowledge of the form of hemodynamic function or the structure of the experimental design is specified. We discuss the rationale and advantages of the proposed approach relative to other exploratory methods, such as clustering or independent component analysis, as well as the differences from methods based on expanded design matrices.