A Generalized Contrast Function and Stability Analysis for Overdetermined Blind Separation of Instantaneous Mixtures

Authors:
Xiao-Long Zhu;Xian-Da Zhang;Ji-Min Ye
Affiliations:
National Laboratory for Information Science and Technology, Department of Automation, Tsinghua University, Beijing 100084, China;National Laboratory for Information Science and Technology, Department of Automation, Tsinghua University, Beijing 100084, China;School of Science, Xidian University, Xi'an 710071, China
Venue:
Neural Computation
Year:
2006

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Abstract

In this letter, the problem of blind separation of n independent sources from their m linear instantaneous mixtures is considered. First, a generalized contrast function is defined as a valuable extension of the existing classical and nonsymmetrical contrast functions. It is applicable to the overdetermined blind separation (m n) with an unknown number of sources, because not only independent components but also redundant ones are allowed in the outputs of a separation system. Second, a natural gradient learning algorithm developed primarily for the complete case (m = n) is shown to work as well with an n × m or m × m separating matrix, for each optimizes a certain mutual information contrast function. Finally, we present stability analysis for a newly proposed generalized orthogonal natural gradient algorithm (which can perform the overdetermined blind separation when n is unknown), obtaining an expectable result that its local stability conditions are slightly stricter than those of the conventional natural gradient algorithm using an invertible mixing matrix (m = n).