A self-organizing map for clustering probabilistic models

We present a general framework for self-organizing maps, which store probabilistic models in map units. We introduce the negative log probability of the data sample as the error function and motivate its use by showing its correspondence to the Kullback-Leibler distance between the unknown true distribution of data and our empirical models. We present a general winner search procedure based on this probability measure and an update step based on its gradients. As an application, we derive the learning rules for a particular probabilistic model that is used in user profiling in mobile communications network. Due to the constrained nature of the parameters of our probabilistic model, we introduce a new parameter space, in which the gradient update step is performed. In the experiments, we show clustering of user profiles using calling data involving normal users of mobile phones and users that are known to be victims of fraud. Finally, we discuss further applications of the approach.