Self-Organizing Maps in data analysis - notes on overfitting and overinterpretation

The Self-Organizing Map, SOM, is a widely used tool in exploratory data analysis. Visual inspection of the SOM can be used to list potential dependencies between variables, that are then validated with more principled statistical methods. In this paper we discuss the use of the SOM in searc hing for dependencies in the data. We poin t out that simple use of the SOM may lead to excessive number of false h ypotheses.We formulate the exact probability densit y model for which the SOM training gives the Maximum Likelihood estimate and show how the model parameters (neighborhood and kernel width) can be chosen to avoid o ver tting.The conditional distributions from the true densit ymodel o er a consisten t w ay to quantify and test the dependencies between variables.