Neural net approach for blind separation of sources based on geometric properties

Abstract

This paper presents a new approach to recover original signals (“sources”) from their linear mixtures, observed by the same number of sensors. The algorithms proposed only assume that the input distributions are bounded. The method is simpler than other proposals and is based on geometric algebra properties. We present a geometric algorithm and a neural network approach to show that with two networks, one for the separation of sources and one for weight learning, running in parallel, it is possible to efficiently recover the original signals. The learning rule is unsupervised and each computational element uses only local information. To achieve the required separation, it is necessary to detect an input vector at each of the edges of the hyperparallelepiped cone that contains the observational space; if this condition is verified the network is able to separate even statistically dependent components of the inputs.