Global convergence of independent component analysis based on semidefinite programming relaxation

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.