Blind source separation using novel independence interpretations for bounded support random vector

Abstract

Amidst the various existingcontrasts for Independent Component Analysis (ICA) and Blind Source Separation (BSS), there remains a demand for a contrast that provides higher accuracy with low computational cost – even when large scale – while remaining unbiased to a particular distribution and robust against outliers and varying sample sizes. Towards this demand, the current article first derives some novel interpretations of statistical independence for bounded support random vectors and then uses those interpretations to develop new class of BSS contrasts. Among them, the $L^2$-norm based contrasts are proved to be robust and estimated directly, in a single stage, using closed-form expressions provided by kernel based linear least squares method. The estimations also serve to extend the existing analogy between Information Theory and Potential Field Theory by introducing a concept of reference information potential. The article uses Genetic Algorithm (GA) and its’ newly derived variant, which is computationally more efficient at higher dimensions, as a global optimization technique within Search for Rotation based ICA (SRICA) algorithm framework. Overall, the simulations prove that the proposed BSS solutions combining the newly derived contrasts with the GA variant for optimization, achieve better separation quality even at large scale and with fewer samples. Furthermore, they remain blind against the distribution of source signals, are robust against outliers, able to avoid misconvergence at local optima, and offer greater accuracy with lower computational cost compared to even exhaustive search methods.