Natural Gradient Learning With A Nonholonomic

This paper addresses natural gradient learning algorithms with a nonholonomic constraint [2] and their application to multichannel blind deconvolution. First, we incorporate a nonholonomic constraintinto the natural gradient learning algorithm for multichannel blind deconvolution that has been developed by Amari-Douglas-Cichocki-Yang [4] and present a slightly modified algorithm whichworks efficiently for the case where weoverestimate the number of sources or the number of sources is not known in advance. Second, we also derive a natural gradient learning algorithm that can be used to train a linear feedback network with FIR synapses. Again, a nonholonomic constraint is incorporated. It is applied to the blind equalization of single input multiple output(SIMO) channels and is compared with the spatio-temporal anti-Hebbian rule [9] which is the extension of the anti-Hebbian rule [16]. The algorithms are rigorously derived and their validity is confirmed by computer simulations