Blind Signal Separation Of Mixtures Of Chaotic Processes: A Comparison Between Independent Component Analysis And State Space Modeling

We perform a systematic comparison between different algorithms for solving the Blind Signal Separation problem. In particular, we compare five well-known algorithms for Independent Component Analysis (ICA) with a recently proposed algorithm based on linear state space modeling (IC-LSS). The comparison is based on simulated mixtures of six source signals, five of which are generated by nonlinear deterministic processes evolving on chaotic attractors. The quality of the reconstructed sources is quantified by two measures, one based on a distance measure implemented by a Frobenius norm, and one based on residual mutual information. We find that the IC-LSS modeling algorithm offers several advantages over the ICA algorithms: it succeeds in unmixing Gaussian sources, on short time series it performs, on average, better than static ICA algorithms, it does not try to remove coincidental dependencies resulting from finite data set size, and it shows the potential to reconstruct the sources even in the case of noninvertible mixing. As expected, for the case of non-Gaussian sources, invertible mixing and sufficient time series length, the ICA algorithms typically outperform IC-LSS modeling.