An energy-based SOM model not requiring periodic boundary conditions

Abstract

We present the Resilient Self-organizing Tissue (ReST) model, a self-organized neural model based on an infinitely often continuously differentiable ($C^\infty$) energy function. ReST extends older work on energy-based self-organizing models (IEEE international conference on neural networks, IEEE, pp 1219–1223, 1993) in several ways. First of all, it converts input–prototype distances into neural activities that are constrained to follow a log-normal distribution. This allows a problem-independent interpretation of neural activities which facilitates, e.g. outlier detection and visualization. And secondly, since all neural activities are constrained in particular to exhibit a predetermined temporal mean, the convolution that is contained in the energy function can be performed using the so-called zero-padding with correction (ZPC) instead of periodic boundary conditions. Since periodic boundary conditions impose much stronger constraints on prototypes, using ReST with ZPC leads to markedly lower quantization errors, especially for small map sizes. Additional experiments are conducted showing the worth of a $C^\infty$ energy function, namely for novelty detection and automatic control of SOM parameters.