General Non-Orthogonal Constrained ICA

Constrained independent component analysis (C-ICA) algorithms have been an effective way to introduce prior information into the ICA framework. The work in this area has focus on adding constraints to the objective function of algorithms that assume an orthogonal demixing matrix. Orthogonality is required in order to decouple—isolate—the constraints applied for each individual source. This assumption limits the optimization space and therefore the separation performance of C-ICA algorithms. We generalize the existing C-ICA framework by using a novel decoupling method that preserves the larger optimization space for the demixing matrix. In addition, this framework allows for the constraining of either the sources or the mixing coefficients. A constrained version of the extended Infomax algorithm is used as an example to show the benefits obtained from the non-orthogonal constrained framework we introduce.