Structure-seeking multilinear methods for the analysis of fMRI data

In comprehensive fMRI studies of brain function, the data structures often contain higher-order ways such as trial, task condition, subject, and group in addition to the intrinsic dimensions of time and space. While multivariate bilinear methods such as principal component analysis (PCA) have been used successfully for extracting information about spatial and temporal features in data from a single fMRI run, the need to unfold higher-order data sets into bilinear arrays has led to decompositions that are nonunique and to the loss of multiway linkages and interactions present in the data. These additional dimensions or ways can be retained in multilinear models to produce structures that are unique and which admit interpretations that are neurophysiologically meaningful. Multiway analysis of fMRI data from multiple runs of a bilateral finger-tapping paradigm was performed using the parallel factor (PARAFAC) model. A trilinear model was fitted to a data cube of dimensions voxels by time by run. Similarly, a quadrilinear model was fitted to a higher-way structure of dimensions voxels by time by trial by run. The spatial and temporal response components were extracted and validated by comparison to results from traditional SVD/PCA analyses based on scenarios of unfolding into lower-order bilinear structures.