Kernel-based equiprobabilistic topographic map formation

We introduce a new unsupervised competitive learning rule, the kernel-based maximum entropy learning rule (kMER), which performs equiprobabilistic topographic map formation 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.