Analytic Comparison of Self-Organising Maps

R. Mayer, D. Baum, R. Neumayer, A. Rauber:
"Analytic Comparison of Self-Organising Maps";
Vortrag: 7th International Workshop on Self-Organizing Maps (WSOM 2009), St. Augustine, Florida, USA; 08.06.2009 - 10.06.2009; in:"Proceedings of the 7th Workshop On Self-Organizing Maps St. Augustine, FL, USA (WSOM 2007)", J. Principe, R. Miikkulainen (Hrg.); Springer, Lecture Notes in Computer Science (2009), ISSN: 0302-9743; S. 182 - 190.

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Abstract:


SOMs have proven to be a very powerful tool for data analysis. However, comparing multiple SOMs trained on the same data set using different parameters or initialisations is still a difficult task. In most cases it is performed only via visual inspection or by utilising one of a range of quality measures to compare vector quantisation or topology preservation characteristics of the maps. Yet, comparing SOMs systematically is both necessary as well as a powerful tool to further analyse data: necessary, because it may help to pick the most suitable SOM out of different training runs; a powerful tool because it allows analysing mapping stabilities across a range of parameter settings. In this paper we present an analytic approach to compare multiple SOMs trained on the same data set. Analysis of output space mapping, supported by a set of visualisations, reveals data co-locations and shifts on pairs of SOMs, considering both different neighbourhood sizes at source and target maps.
A similar concept of mutual distances and relationships can be analysed at a cluster level. Finally, Comparisons aggregated automatically across several SOMs are strong indicators for strength and stability of mappings.