CASOM: SOM for Contingency Tables and Biplot

This article presents a new way of dealing with the self-organizing map methods to visualize by an original way qualitative data or histogram vectors as we can find on the Internet e.g. after the pre-processing of plain text documents. The main difference with other known methods is the nature of the processed matrix: a contingency table. By adding constraints during the learning of a mixture of a discrete distribution which models the noise in classes of documents or rows, we obtain a self-organizing map algorithm named CASOM. We explain the properties of the model: metrics, criteria, links with Correspondence Analysis and mean biplot which help to better interpret results. A more general projection available for self-organizing maps in the dual Euclidian space or columns is also introduced. Then, we present some experiments on a corpus of textual short summaries to illustrate the behavior of the algorithm and to show its interest. The conclusion discusses alternative models and gives perspectives of the contribution.