A BRUTE-FORCE ANALYTICAL FORMULATION OF THE INDEPENDENT COMPONENTS ANALYSIS SOLUTION
Deniz Erdoğmuş, Anant Hegde, Kenneth E. Hild, Mustafa C. Ozturk, José Carlos Príncipe · 2003
Many algorithms based on information theoretic measures and/or temporal statistics of the signals have been proposed for ICA in the literature. There have also been analytical solutions suggested based on predictive modeling of the signals. In this paper, we show that finding an analytical solution for the ICA problem through solving a system of nonlinear equations is possible. We demonstrate that this solution is robust to decreasing sample size and measurement SNR. Nevertheless, finding the root of the nonlinear function proves to be a challenge. Besides the analytical solution approach, we try finding the solution using a least squares approach with the derived analytical equations. Monte Carlo simulations using the least squares approach are performed to investigate the effect of sample size and measurement noise on the performance.