Global analysis of log likelihood criterion

Authors:
Gen Hori
Affiliations:
Brain Science Institute, RIKEN, Saitama, Japan
Venue:
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Year:
2006

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Abstract

This paper introduces and investigates a gradient flow of the log likelihood function restricted on the isospectral submanifold and proves that the flow globally converges to diagonal matrices for almost all positive definite initial matrices. This result shows that the log likelihood function does not have any spurious stable fixed point and ensures the global convergence of ICA algorithms based on the log likelihood function.