A hidden Markov model for metric and event-based data

The question of data representation is central to any data analysis problem. Ideally, the representation should faithfully describe the domain to be analyzed and in addition, the model used should be able to process such a representation. In practice, however, the modeler must often compromise how the problem is described, since the class of possible representations is constrained by the model. This problem may be circumvented by extending conventional models to handle more unconventional data representations. These data are often found in industrial environments and especially in telecommunications. In this paper, we consider an extension of hidden Markov models (HMM) for modeling data streams, which switch between metric and event-based representations. In a HMM, the representation of the observed data is constrained by the emission probability density. Since this density can not change its representation once it is fixed, modeling data streams involving different types of data semantics can be difficult. In the extension introduced in this paper, an additional data semantics variable is introduced, which is conditional on the hidden variable. Furthermore, data itself is conditioned on its semantics, which enables correct interpretation of the observed data. We briefly review the essentials of HMMs and present our extended architecture. We proceed by introducing inference and learning rules for the extension. As an application, we present a HMM for user profiling in mobile communications networks, where the data exhibits switching behavior.