Nonlinear Spring Model of Self-Organizing Map and its Chaotic Behavior

Abstract The Self-Organizing Map (SOM) is an unsupervised neural network introduced by Kohonen and is a model simplifying self-organization process of the brain. However, SOM is still far away from the realization of the brain mechanism. In order to realize more powerful and more flexible mechanism, it is important to propose new models of the brain mechanism and to investigate their behaviors. In this study, as the first step to realize a new nonlinear spring model of SOM, we propose a simple one dimensional 2-neuron model connected by a non-linear spring. We investigate its behavior under a simple assumption where input vectors are given to the model periodically. Furthermore, in order to investigate the behavior of the nonlinear spring model of SOM, we calculate one-parameter bifurcation diagram and the largest Lyapunov exponent of the proposed model. Computer simulated results show that the neurons oscillate chaotically. Key words Self-Organizing Maps (SOM), Clustering, Data Mining 1