Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Adaptive blind separation of independent sources: a deflation approach
Signal Processing
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
A Further Result on the ICA One-Bit-Matching Conjecture
Neural Computation
One-Bit-Matching Conjecture for Independent Component Analysis
Neural Computation
A Constrained EM Algorithm for Independent Component Analysis
Neural Computation
Analysis of the Kurtosis-Sum Objective Function for ICA
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
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The one-bit-matching conjecture for independent component analysis (ICA) has been widely believed in the ICA community. Theoretically, it has been proved that under certain regular assumptions, the global maximum of a simplified objective function derived from the maximum likelihood or minimum mutual information criterion under the one-bit-matching condition corresponds to a feasible solution of the ICA problem, and also that all the local maxima of the objective function correspond to the feasible solutions of the ICA problem in the two-source square mixing setting. This paper further studies the one-bit-matching conjecture along this direction, and we prove that under the one-bit-matching condition there always exist many local maxima of the objective function that correspond to the stable feasible solutions of the ICA problem in the general case; moreover, in ceratin cases there also exist some local minima of the objective function that correspond to the stable feasible solutions of the ICA problem with mixed super- and sub-Gaussian sources.