Multiplicative nonholonomic/Newton-like algorithm

We construct new algorithms, which use the fourth order cumulant of stochas tic variables for the cost function. The multiplicative updating rule here constructed is natural from the homogeneous nature of the Lie group and has numerous merits for the rigorous treatment of the dynamics. As one consequ ence, the second order convergence is shown. For the cost function, functio ns invariant under the componentwise scaling are chosen. By identifying poi nts which can be transformed to each other by the scaling, we assume that t he dynamics is in a coset space. In our method, a point can move toward any direction in this coset. Thus, no prewhitening is required. (C) 2001 Elsev ier Science Ltd. All rights reserved.