Generative Probability Density Model in the Self-Organizing Map

The Self-Organizing Map, SOM, is a widely used tool in exploratory data analysis. A theoretical and practical challenge in the SOM has been the diffi­ culty to treat the method as a statistical model fitting procedure. In this chapter we give a short review of statistical approaches for the SOM. Then we present the probability density model for which the SOM training gives the maximum likeli­ hood estimate. The density model can be used to choose the neighborhood width of the SOM so as to avoid overfitting and to improve the reliability of the results. The density model also gives tools for systematic analysis of the SOM. A major ap­ plication of the SOM is the analysis of dependencies between variables. We discuss some difficulties in the visual analysis of the SOM and demonstrate how quanti­ tative analysis of the dependencies can be carried out by calculating conditional distributions from the density model.