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. 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. Instead of successively selecting paired columns of the unitary diagonalizing matrix U to which to apply planar Givens rotations (as in the original JADE algorithm), we sequentially process the columns of U and maximize the JADE criterion with respect to each individual column separately. We utilize the unitary property of U and achieve decoupling of its columns via orthogonal projections. We propose a method called Alternating Eigen-search (AE) to maximize the JADE criterion one column at a time. The method is extended to the case in which there are application-dependent quadratic constraints imposed on the mixing matrix, resulting in the so-called constrained ICA. Example results are provided to demonstrate the effectiveness and applicability of the algorithm.