Compressive Independent Component Analysis

In this paper we investigate the minimal dimension statistic necessary in order to solve the independent component analysis (ICA) problem. We create a compressive learning framework for ICA and show for the first time that the memory complexity scales only quadratically with respect to the number of independent sources n, resulting in a vast improvement over other ICA methods. This is made possible by demonstrating a low dimensional model set, that exists in the cumulant based ICA problem, can be stably embedded into a compressed space from a larger dimensional cumulant tensor space. We show that identifying independent source signals can be achieved with high probability when the compression size m is of the optimal order of the intrinsic dimension of the ICA parameters and propose a iterative projection gradient algorithm to achieve this.