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Global convergence of independent component analysis based on semidefinite programming relaxation

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2 Author(s)
Shotaro Akaho ; The National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8568 Japan ; Jun Fujiki

In the independent component analysis, polynomial functions of higher order statistics are often used as cost functions. However, such cost functions usually have many local minima, hence gradient-type and fixed-point-type algorithms tend to be trapped into a nonglobal local minimum. Recently, the polynomial optimization method that guarantees global convergence has been developed, where the optimization problem is relaxed as a semidefinite programming problem. In this paper, we apply the polynomial optimization method to the independent component analysis, and show the global convergence property. From some empirical studies, we further give a conjecture that the algorithm has polynomial time computational complexity.

Published in:

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Date of Conference:

22-27 May 2011