Mathematical problems in the application of multilinear models to facial emotion processing experiments

In this paper we describe the enormous potential that multilinear models hold for the analysis of data from neuroimaging experiments that rely on functional magnetic resonance imaging (fMRI) or other imaging modalities. A case is made for why one might fully expect that the successful introduction of these models to the neuroscience community could define the next generation of structure-seeking paradigms in the area. In spite of the potential for immediate application, there is much to do from the perspective of statistical science. That is, although multilinear models have already been particularly successful in chemistry and psychology, relatively little is known about their statistical properties. To that end, our research group at the University of Kentucky has made significant progress. In particular, we are in the process of developing formal influence measures for multilinear methods as well as associated classification models and effective implementations. We believe that these problems will be among the most important and useful to the scientific community. Details are presented herein and an application is given in the context of facial emotion processing experiments.