Distance between Kohonen Classes Visualization Tool to Use SOM in Data Set Analysis and Representation

Abstract

Representation of information given by clustering methods is of little satisfaction. Some tools able to localize classes into the input space are expected in order to provide a good visual support to the analysis of classification results. Actually, clusters are often visualized with the planes produced by factorial analysis. These representations are sometimes unsatisfying, for example when the intrinsic structure of the data is not at all linear or when the compression phenomenon generated by projections on factorial planes is very important. In the family of clustering methods, the Kohonen algorithm has the originality to organize classes considering the neighborhood structure between them [9][10][6]. It is interesting to notice that many transcription in graphical display have been conceived to optimize the visual exploitation of this neighborhood structure [5][11]. Each one helps the interpretation in a particular context. they are twinned to the Kohonen algorithm and called Kohonen maps. For example, one used in the following helps the interpretation of the classification from an exogenous or endogenous qualitative variable. Unfortunately, no one allows for a visualization of the data set structure in the input space. This is very regrettable when the Kohonen map makes such a folder that two classes close to each other in the input space can be far on the map. A tool that visualizes distances between all classes gives a representation of the classification structure in the input space. Such a tool is proposed in the following. As the Kohonen algorithm has the property to reveal effects of small distances also called local distances and the new tool is able to control big distances, this clustering method has now a large field of exploitation.