Analytic Comparison of Self-Organising Maps

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 leaps. 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.