A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Well-known linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1

A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feed-forward memory connections, wideband array processing, and in problems with a multi-input, multi-output network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...

Recently, several neural algorithms have been introduced for Independent Component Analysis. Here we approach the problem from the point of view of a single neuron. First, simple Hebbian-like learning rules are introduced for estimating one of the independent components from sphered data. Some of the learning rules can be used to estimate an independent component which has a negative kurtosis, and the others estimate a component of positive kurtosis. Next, a two-unit system is introduced to estimate an independent component of any kurtosis. The results are then generalized to estimate independent components from non-sphered (raw) mixtures. To separate several independent components, a system of several neurons with linear negative feedback is used. The convergence of the learning rules is rigorously proven without any unnecessary hypotheses on the distributions of the independent components.

this paper, we adopt the neural network approach. The main objective of this paper is threefold. 1. To present (in Section 2) a neural network and propose unconstrained extraction and deflation criteria that do not require either a priori knowledge of source signals or whitening of mixed signals, and can cope with a mixture of signals with positive kurtosis and signals with negative kurtosis. These criteria should lead to simple, very efficient, purely local, and biologically plausible learning rules (Hebbian/anti-Hebbian type learning algorithms) . 2. To prove (in Section 3) analytically that the proposed criteria have no spurious equilibria. In other words, the resulting learning rules always reach desired solutions, regardless of initial conditions. 3. To demonstrate (in Section 4) with computer simulations the validity and high performance for practical use of the presented neural network and associated learning algorithms.

Two alternative neural-network methods are presented which both extract independent source signals one-byone from a linear mixture of sources when the number of mixed signals is equal to or larger than the number of sources. Both methods exploit the previously extracted source signals as a priori knowledge so as to prevent the same signals from being extracted several times. One method employs a deflation technique which eliminates from the mixture the already extracted signals and another uses a hierarchical neural network which avoids duplicate extraction of source signals by inhibitory synapses between units. Extensive computer simulations confirm the validity and high performance of our methods. 1. INTRODUCTION Blind source separation can be formulated as the task to recover the unknown sources from the sensor signals described by x(t) = As(t); where x(t) is an n 2 1 sensor vector, s(t) is an m 2 1 unknown source vector having independent and zero-mean signals, and A is an n 2 m ...

Two alternative neural-network methods are presented which both extract independent source signals one-byone from a linear mixture of sources when the number of mixed signals is equal to or larger than the number of sources. Both methods exploit the previously extracted source signals as a priori knowledge so as to prevent the same signals from being extracted several times. One method employs a de ation technique which eliminates from the mixture the already extracted signals and another uses a hierarchical neural network which avoids duplicate extraction of source signals by inhibitory synapses between units. Extensive computer simulations con rm the validity and high performance of our methods. 1.

SUMMARY We present a cascade neural network for blind source extraction. We propose a family of unconstrained optimization criteria, from which wederivealearning rule that can extract a single source signal from a linear mixture of source signals. To prevent the newly extracted source signal from being extracted again in the next processing unit, we propose another unconstrained optimization criterion that uses knowledge of this signal. From this criterion, we then derive a learning rule that de ates from the mixture the newly extracted signal. By virtue of blind extraction and de ation processing, the presented cascade neural network can cope with a practical case where the number of mixed signals is equal to or larger than the number of sources, with the number of sources not known in advance. We prove analytically that the proposed criteria both for blind extraction and de ation processing have no spurious equilibria. In addition, the proposed criteria do not require whitening of mixed signals. We also demonstrate the validity and performance of the presented neural network by computer simulation experiments. key words: blind source separation and extraction, neural networks, on-line adaptive algorithms 1.