A New Learning Algorithm for Blind Signal Separation

TLDR

The source signals and mixing matrix are unknown except for the number of sources. The study derives a new online learning algorithm that minimizes statistical dependency among outputs for blind separation of mixed signals and proposes a novel activation function with equivariant properties for easy implementation on a neural network‑like model. The algorithm measures dependency via average mutual information of outputs, evaluates it using a Gram‑Charlier expansion instead of Edgeworth, and minimizes it with a natural gradient approach. Computer simulations confirm the validity of the new learning algorithm.

Abstract

A new on-line learning algorithm which minimizes a statistical dependency among outputs is derived for blind separation of mixed signals. The dependency is measured by the average mutual information (MI) of the outputs. The source signals and the mixing matrix are unknown except for the number of the sources. The Gram-Charlier expansion instead of the Edgeworth expansion is used in evaluating the MI. The natural gradient approach is used to minimize the MI. A novel activation function is proposed for the on-line learning algorithm which has an equivariant property and is easily implemented on a neural network like model. The validity of the new learning algorithm are verified by computer simulations.