Power-CCA: Maximizing the Correlation Coefficient between the Power of Projections
This work presents a variation of canonical correlation analysis (CCA), where the correlation coefficient between the instantaneous power of the projections is maximized, rather than between the projections themselves. The resulting optimization problem is not convex, and we have to resort to a sub-optimal approach. Concretely, we propose a two-step solution consisting of the singular value decomposition (SVD) of a "coherence" matrix followed by a rank-one matrix approximation. This technique is applied to blindly recovering signals in a model that is motivated by the study of neuronal dynamics in humans using electroencephalography (EEG) and magnetoencephalography (MEG). A distinctive feature of this model is that it allows recovery of amplitude-amplitude coupling between neuronal processes.