A new algorithm for independent component analysis with or without constraints

A new algorithm is developed for independent component analysis (ICA) with or without constraints on the mixing matrix or sources. The algorithm is based on the criterion of Joint Approximate Diagonalization of Eigen-matrices (JADE). We propose a column-wise processing approach to perform joint diagonalization of the cumulant (eigen-) matrices. We utilize the unitary property of diagonalizing matrix U and achieve decoupling of its columns via orthogonal projections. We propose a method called Alternating Eigen-search (AE) to maximize the JADE criterion with respect to one column of U at a time. The method is extended to the case in which there are application-dependent quadratic constraints imposed on the mixing matrix or sources, resulting in the so-called constrained ICA. Example results are provided to demonstrate the effectiveness and applicability of the algorithm.