Normalization Processes an Topographic Mapping Model between Cell Layers Represented by Undirected Graphs

Abstract

We propose simple topographic mapping formation models from cell layer to cell layer. Our model is a discrete one, that is the state value of input and output cells takes 0 or 1 and input and output layers are represented by undirected graphs. Thus, a topographic mapping described in this model is a map which preserves the adjacency relation. We define several learning rules and a few weight normalization methods. By computer simulations we investigate topographic mapping formation conditions. We show that when an output unit normalization is considered, we have more learning rules which yield topographic mappings than the cases when an input normalization is adopted or without normalization. As to the input unit normalization, we have shown theoretically that topographic mappings are the only stable ones under the correlational type learning rule.