Multidimensional independent component analysis using characteristic functions

The goal of multidimensional independent component analysis (MICA) lies in the linear separation of data into statistically independent groups of signals. In this work, we give an elementary proof for the uniqueness of this problem in the case of equally sized subspaces, showing that the separation matrix is essentially unique except for row permutation and scaling. The proof is based on the reinterpretation of groupwise independence as factorization of the joint characteristic function. We then employ this property to propose a novel algorithm for robustly performing MICA. Simulation results demonstrate the reliability of our method.