Distance between Kohonen classes: Visualization of data set structure with SOM

By Patrick Rousset, Christiane Guinot.

Abstract: SOM is an often-used clustering method that mirrors the topology between classes with a map. Many tools superimpose on this map endogenous or exogenous information in order to integrate this topology in the data analysis. A new tool, that we present here, displays the results of the computation of the distances between all centro´ds, which simplifies the distance-matrix contents by managing the redundancy. Therefore, this tool allows an interpretation in the input space by visualising the intrinsic structure of the data. The SOM becomes then an efficient non-linear multidimensional data analysis method including graphical representations. As an application, the Kohonen map is used to chart any classification in the input space. This method is particularly well adapted when the intrinsic structure of the data is not linear at all, and can eventually supply classical linear techniques. Furthermore, SOM can be perceived as a technique of data set adjustment with a surface including its own graphical representation.

Key Words: Classification, Data set representation, Kohonen maps, Multivariate data analysis, Neural networks, SOM

Authors:
Patrick Rousset, rousset@cereq.fr
Christiane Guinot, christiane.guinot@ceries-lab.fr

Editor: Avner Bar-Hen,avner@bar-hen.net

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