A combination of parallel factor and independent component analysis

Although CPA (Canonical/Parallel factor Analysis) provides a unique decomposition, the actual computation can be made more robust by incorporating extra constraints. In several applications, the factors in one mode are known to be statistically independent. On the other hand, in Independent Component Analysis (ICA), it often makes sense to impose a Khatri-Rao structure on the mixing vectors. In this paper, we propose a new algorithm to impose independence constraints in CPA. Our algorithm implements the algebraic CPA structure and the property of statistical independence simultaneously. Numerical experiments show that our method outperforms in several cases ordinary CPA and ICA. We also present a strategy for imposing (partial) symmetry in CPA.