SOM Quality Measures: An Efficient Statistical Approach

We are interested in practical tools for the quantitative evaluation of self-organizing maps (SOMs). Recently it has been argued that any quality measure for SOMs needs to evaluate the embedding or coverage of a map as well as its topological quality. Over the years many different quality measures for self-organizing maps have been proposed. However, many of these only measure one aspect of a SOM or are computationally very expensive or both. Here we present a novel, computationally efficient statistical approach to the evaluation of SOMs. Our approach measures both the embedding and the topological quality of a SOM.