A method to evaluate topological information of self-organizing maps

抄録

The aim of self-organizing maps (SOM) is to obtain a topology-preserving mapping from high-dimensional invisible feature space to two or less dimensional visible space. With a preferable mapping, all topological information of the feature space is visible. However, SOM loses topological information to some extent in most cases. This paper proposes a new method to evaluate topology preservation of SOMs. SOM is regarded as a pair of graphs on common vertices and different edges. Amount of visible information of adjacency in the feature space is evaluated as mutual information of simultaneous probability distribution on edges of the paired graphs.