Global convergence of independent component analysis based on semidefinite programming relaxation
Shotaro Akaho, Jun Fujiki · 2011
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.