Evolutionary Self-Organizing Map

An evolutionary self-organizing map is presented. The evolutionary training algorithm operates on a two-dimensional population grid that has sample points to guide the search. As a result of competition and locally guided evolution the network is able to create organization among individuals. For visual validation of the algorithm, a two-dimensional data example is presented. Competitive learning is a powerful paradigm. For example, self-organizing maps (SOM) Kohonen 1995] use competitive learning to cause organization between prototypes. On the other hand, in evolutionary computing competitive learning causes structural optimization in a population of individuals Goldberg 1989], Michalewicz 1992]. Now a question arises: Can these ideas be put together to form an algorithm causing both structural optimization, and self-organization of alternative structures at the same time? What would be the beneets of this kind of an algorithm? In complex cases there is rarely just one correct optimal solution to a problem. Rather there are several good solutions for diierent conditions. A good example would be indentiication of nonlinear processes using time-series modeling Ljung 1987]: models with diierent model orders and delays are needed for diierent operating conditions. Rather than having just one model, one needs a collection of models to represent the whole operation regime of the process. In short, the objective is to have an algorithm that is able to carry out structural optimization of complex objects and create organization among them. The objectives of previous work combining SOM and evolu-seem to have been diierent, i.e. evolutionary computing has been used to optimize the topological structure of the SOM, and standard learning algorithm has been used to train the self-organizing map. A short suggestion to the direction of evolutionary learning of SOM can be found in Kohonen 1995, p. 159]. However, no exact algorithm or examples are given. In this work the fundamental idea is to use the spatial grid structure of the SOM as an evolutionary platform where individuals are interacting and evolving, thus creating organization. The organization is directed by the scalar tness values of the individuals. The structure of the individuals is of no concern, making it possible to extend the applications of self-organizing maps. An application of the idea to dynamic modeling can be found in Nissinen 1998], for example. The paper is organized as follows: The Section II presents the data structure of the algorithm. In Section III the training algorithm is given, whose performance is demonstrated …