International Journal of Neural Systems, Vol. 7, Nos. 6 (1997) 671
© World Scientific Publishing Company
International Journal of Neural Systems, Vol. 7, Nos. 6 (1997) 671
© World Scientific Publishing Company
Recently, several neural algorithms have been
introduced for Independent Component Analysis. Here we approach
the problem from the point of view of a single neuron. First,
simple Hebbian-like learning rules are introduced for estimating
one of the independent components from sphered data. Some of the
learning rules can be used to estimate an independent component
which has a negative kurtosis, and the others estimate a
component of positive kurtosis. Next, a two-unit
system is introduced to estimate an independent component of any
kurtosis. The results are then generalized to estimate
independent components from non-sphered (raw) mixtures. To
separate several independent components, a system of several
neurons with linear negative feedback is used. The convergence
of the learning rules is rigorously proven without any
unnecessary hypotheses on the distributions of the independent
components.