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Blind separation of positive sources by globally convergent gradient search

Oja, E and Plumbley, M (2004) Blind separation of positive sources by globally convergent gradient search NEURAL COMPUTATION, 16 (9). pp. 1811-1825.

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Abstract

The instantaneous noise-free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix. However, with some prior information on the sources, like positivity, new analysis and perhaps simplified solution methods may yet become possible. In this letter, we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded, which means that they have a nonzero pdf in the region of zero. It can be shown that in this case, the solution method is basically very simple: an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources. We propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint, under which the separating matrix is orthogonal. We further prove that in the Stiefel manifold of orthogonal matrices, the cost function is a Lyapunov function for the matrix gradient flow, implying global convergence. Thus, this algorithm is guaranteed to find the nonnegative well-grounded independent sources. The analysis is complemented by a numerical simulation, which illustrates the algorithm.

Item Type: Article
Subjects : Electronic Engineering
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
AuthorsEmailORCID
Oja, EUNSPECIFIEDUNSPECIFIED
Plumbley, MUNSPECIFIEDUNSPECIFIED
Date : 1 September 2004
Identification Number : https://doi.org/10.1162/0899766041336413
Copyright Disclaimer : Copyright 2004 Massachusetts Institute of Technology
Uncontrolled Keywords : Science & Technology, Technology, Computer Science, Artificial Intelligence, Computer Science, COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE, NEUROSCIENCES, INDEPENDENT COMPONENT ANALYSIS, MATRIX FACTORIZATION, CONSTRAINTS, ALGORITHMS
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 13 Sep 2016 09:16
Last Modified : 13 Sep 2016 09:16
URI: http://epubs.surrey.ac.uk/id/eprint/812113

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