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Topology analysis of data space using self-organizing feature map

In order to analyze the topological structure of the data space using Kohonen's self-organizing feature map, a criterion is discussed. The Euclidian distance between the reference vector and the data, the number of the reference vectors and the topology preserving measure are taken into account and combined in a unified criterion. Through computer simulation, it is confirmed that goodness of the different reference topologies, that is dimensions, can be clearly discriminated regardless the parameters. Thus, the unified criterion described makes it possible to analyze the essential data space topology.