Neural Computation, Vol 10, 1847-1871, Copyright © 1998 by The MIT Press

LETTERS

Kernel-Based Equiprobable Topographic Map Formation

Marc M. Van Hulle

We introduce a new unsupervised competitive learning rule, the kernel-based maximumentropy learning rule (kMER), whichperforms equiprobabilistic topographic mapformation in regular, fixed-topology lattices, for use with nonparametric density estimation as well as nonparametric regression analysis. The receptive fields of the formal neurons are overlapping radially symmetric kernels, compatible with radial basis functions (RBFs); but unlike other learning schemes, the radii of these kernels do not have to be chosen in an ad hoc manner: the radii are adapted to the local input density, together with the weight vectors that define the kernel centers, so as to produce maps of which the neurons have an equal probability to be active (equiprobabilistic maps). Both an "online" and a "batch" version of the learning rule are introduced, which are applied to nonparametric density estimation and regression, respectively. The application envisaged is blind source separation (BSS) from nonlinear, noisy mixtures.

This article has been cited by other articles:

				J. C. Claussen Winner-Relaxing Self-Organizing Maps Neural Comput., May 1, 2005; 17(5): 996 - 1009. [Abstract] [Full Text] [PDF]

				M. M. Van Hulle Maximum Likelihood Topographic Map Formation Neural Comput., March 1, 2005; 17(3): 503 - 513. [Abstract] [Full Text] [PDF]

				M. M. Van Hulle Joint Entropy Maximization in Kernel-Based Topographic Maps Neural Comput., August 1, 2002; 14(8): 1887 - 1906. [Abstract] [Full Text] [PDF]

				M. M. Van Hulle Kernel-Based Topographic Map Formation by Local Density Modeling Neural Comput., July 1, 2002; 14(7): 1561 - 1573. [Abstract] [Full Text] [PDF]