Using Particle Swarm Optimization for Minimizing Mutual Information in Independent Component Analysis

Independent Component Analysis (ICA) aims to recover a set of independent random variables starting from observations that are a mixture of them. Since the prior knowledge of the marginal distributions is unknown with the only restriction of at most one Gaussian component, the problem is usually formulated as an optimization one, where the goal is the maximization (minimization) of a cost function that in the optimal value approximates the statistical independence hypothesis. In this paper, we consider the ICA contrast function based on the mutual information. The stochastic global Particle Swarm Optimization (PSO) algorithm is used to solve the optimization problem. PSO is an evolutionary algorithm where the potential solutions, called particles, fly through the problem space by following the current optimum particles. It has the advantage that it works for non-differentiable functions and when no gradient information is available, providing a simple implementation with few parameters to adjust. We apply successfully PSO to separate some selected benchmarks signals.