Evolving High-Posterior Self-Organizing Maps

Bayesian inference for neural networks has received a good deal of attention in recent years. Unlike standard methods, the bayesian approach provides the analyst with the richness (and complexity) of a probability distribution over the space of network weights (and possibly other quantities of interest). These posterior distributions prompt an optimization problem that may be suitable for evolutionary algorithms. This possibility is obviously of foremost interest when no alternative global functions are available for optimization. Some preliminary results related to one of such cases, namely, the self-organizing map, are presented in this paper. Specifically, a familiar "Steady-state" diffusion genetic algorithm is described and tested.

[1]  Thomas Villmann,et al.  Neural maps and topographic vector quantization , 1999, Neural Networks.

[2]  Christopher M. Bishop,et al.  GTM: The Generative Topographic Mapping , 1998, Neural Computation.

[3]  Peter Müller,et al.  Issues in Bayesian Analysis of Neural Network Models , 1998, Neural Computation.

[4]  T. Samad,et al.  Genetic optimization of self-organizing feature maps , 1991, IJCNN-91-Seattle International Joint Conference on Neural Networks.

[5]  Jorge Muruzábal,et al.  On the Visualization of Outliers via Self-Organizing Maps , 1997 .

[6]  Anil K. Jain,et al.  A nonlinear projection method based on Kohonen's topology preserving maps , 1992, IEEE Trans. Neural Networks.

[7]  Daniel Polani,et al.  Training Kohonen Feature Maps in Different Topologies: An Analysis Using Genetic Algorithms , 1993, ICGA.

[8]  Jorma Laaksonen,et al.  SOM_PAK: The Self-Organizing Map Program Package , 1996 .

[9]  Anne Lohrli.  Chapman and Hall , 1985 .

[10]  Yuval Davidor,et al.  A Naturally Occurring Niche and Species Phenomenon: The Model and First Results , 1991, ICGA.

[11]  Akio Utsugi.  Hyperparameter Selection for Self-Organizing Maps , 1997, Neural Computation.

[12]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[13]  Luisa Franconi,et al.  Comparison of a genetic algorithm and simulated annealing in an application to statistical image reconstruction , 1997, Stat. Comput..

[14]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .