Trilinear Modeling of Event-Related Potentials

This paper describes a method for estimating a set of spatial components (brain maps) and temporal components (waveforms) of brain potentials. These components play the role of bases of a coordinate system, in the sense that the brain potentials of any subject can be represented as superpositions of these components. The representation is unique given the spatial and temporal components, and this decomposition is particularly appealing for comparing the brain potentials of different subjects (say alcoholics and controls). It can also be used for single trial modeling, clinical classification of patients, and data filtering. The method is based on the topographic component model (TCM, Möcks 1988) which models brain potentials in a trilinear form. We extend the TCM in two aspects. First, the diagonal amplitude matrix is replaced by a general loading matrix based on some neurophysiological considerations. Secondly, the number of spatial components and the number of temporal components can be different. The spatial components and temporal components are obtained respectively by performing singular value decomposition (SVD). This method is illustrated with visual P3 data.