Some global and local convergence analysis on the information-theoretic independent component analysis approach

In this paper, we present a detailed theoretical analysis on the information-theoretic Independent Component Analysis (IT-ICA) approach. We "rst provide a number of lemmas and theorems on properties of the corresponding cost function in the general n-channel case with di!erentiable, odd, monotonic decreasing nonlinearity. A theorem on behaviour of the cost function along a radially outward line is given for characterizing the global con"guration of the cost function in the parameter space. Furthermore, on the 2-channel IT-ICA system with cubic nonlinearity, we not only exhaustively solve out all equilibrium points and the condition for stability, but also give a global convergence theorem. ( 2000 Elsevier Science B.V. All rights reserved.