On the Decomposition of the Self-Organizing Map Distortion Measure

Assessment of model properties with respect to data is important for reliable analysis of data. After training, Self-Organizing Map (SOM) can be assessed, for instance, with respect to its quantization or its topology preservation properties with onenumber summaries. In this paper, we present a decomposition of the SOM distortion measure for measuring different aspects of the SOM for map units locally. The terms measure quantization quality, the goodness of topological preservation, and the stress between these two aspects. Experiments are used to illustrate the behavior of the distortion measure terms in different error scenarios.