Abstract
One year ago, the Jutten-Herault (JH) network was the only existing tool for recovering p stochastic “source” processes from an unknown mixture [1]. With guidance provided by neurosciences analogies, the unsupervised learning JH algorithm has been adjusted and implemented on an array of p linear neurons totally interconnected [0] [1]. Because of its numerous applications ranging from image processing to antenna array processing, the JH algorithm received much attention during the last few years [2], but no rigorous derivation has been proposed to date. We attempt in this paper to analyze it from a statistics point of view. For instance, it could be shown that the updating term of the synaptic efficacies matrix, δC, cannot be the gradient of a single C2 functional contrary to what is sometimes understood. In fact, we show that the JH algorithm is actually searching common zeros of p functionals by a technique of Robbins-Monro type.
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This work was supported by DRET, Paris, France
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References
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Comon, P.: Separation of Stochastic Processes whose Linear Mixture is Observed, ONRNSF-IEEE Workshop on Higher-Order Spectral Analysis, Vail, Colorado, (june 28–30, 1989).
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© 1990 Springer-Verlag Berlin Heidelberg
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Comon, P. (1990). Statistical approach to the Jutten-Hérault algorithm. In: Soulié, F.F., Hérault, J. (eds) Neurocomputing. NATO ASI Series, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76153-9_9
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DOI: https://doi.org/10.1007/978-3-642-76153-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-76155-3
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