How to use the Kohonen algorithm to simultaneously analyze individuals and modalities in a survey

The Kohonen algorithm (SOM, Self-Organization and Associative Memory, Springer Series in Information Sciences, vol. 8, Springer, Berlin, 1984; Self-Organizing Maps, Springer Series in Information Science, vol. 30, Springer, Berlin, 1995) is a very powerful tool for data analysis. It was originally designed to model organized connections between some biological neural networks. It was also immediately considered as a very good algorithm to realize vectorial quantization, and at the same time pertinent classification, with nice properties for visualization. If the individuals are described by quantitative variables (ratios, frequencies, measurements, amounts, etc.), the straightforward application of the original algorithm leads to build code vectors and to associate to each of them the class of all the individuals which are more similar to this code-vector than to the others. But, in case of individuals described by categorical (qualitative) variables having a finite number of modalities (like in a survey), it is necessary to define a specific algorithm. In this paper, we present a new algorithm inspired by the SOM algorithm, which provides a simultaneous classification of the individuals and of their modalities.