Analyzing and representing multidimensional quantitative and qualitative data: Demographic study of the Rhône valley. The domestic consumption of the Canadian families

The SOM algorithm is now extensively used for data mining, representation of multidimensional data and analysis of relations between variables. With respct to any other classification method, the main characteristic of the SOM classification is the conservation of the topology: after learning, "close" observations are associated to the same class or to "close" classes according to the definition of the neighborhood in the SOM network. This feature allows to consider the resulting classification as a good starting point for further developments as shown in what follows. But in fact its capabilities have not been fully exploited so far. In this chapter, we present some of the techniques that can be derived from the SOM algorithm: the representation of the classes contents, the visualization of the distances between classes, a rapid and robust two-level classification based on the quantitative variables, the computation of clustering indicators, the crossing of the classification with some qualitative variables to interpret the classification and give prominence to the most important explanatory variables. We also define two original algorithms (KORRESP and KACM) to analyze the relations between qualitative variables.