Entropy-based kernel mixture modeling for topographic map formation

A new information-theoretic learning algorithm for kernel-based topographic map formation is introduced. In the one-dimensional case, the algorithm is aimed at uniformizing the cumulative distribution of the kernel mixture densities by maximizing its differential entropy. A nonparametric differential entropy estimator is used on which normalized gradient ascent is performed. Both differentiable and nondifferentiable kernels are in principle supported, such as Gaussian and rectangular (on/off) kernels. The relation is shown with joint entropy maximization of the kernel outputs. The learning algorithm´s performance is assessed and compared with the theoretically optimal performance. A fixed-point rule is derived for the case of heterogeneous kernel mixtures. Finally, an extension of the algorithm to the multidimensional case is suggested.