Abstract
We present an approach for blindly decomposing an observed random vector x into f(As) where f is a diagonal function i.e. f = f 1×... ×f m with one-dimensional functions f i and A an m× n matrix. This postnonlinear model is allowed to be overcomplete, which means that less observations than sources (m<n) are given. In contrast to Independent Component Analysis (ICA) we do not assume the sources s to be independent but to be sparse in the sense that at each time instant they have at most m–1 non-zero components (Sparse Component Analysis or SCA). Identifiability of the model is shown, and an algorithm for model and source recovery is proposed. It first detects the postnonlinearities in each component, and then identifies the now linearized model using previous results.
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© 2004 Springer-Verlag Berlin Heidelberg
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Theis, F.J., Amari, Si. (2004). Postnonlinear Overcomplete Blind Source Separation Using Sparse Sources. In: Puntonet, C.G., Prieto, A. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2004. Lecture Notes in Computer Science, vol 3195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30110-3_91
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DOI: https://doi.org/10.1007/978-3-540-30110-3_91
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