Proportional data modeling with hidden Markov models based on generalized Dirichlet and Beta-Liouville mixtures applied to anomaly detection in public areas

•Derivation of the equations of a generalized Dirichlet-based hidden Markov model.•Derivation of the equations of a Beta-Liouville-based hidden Markov model.•Application of the new models to public areas surveillance scenarios.•Better performance over the Dirichlet-based hidden Markov models.•Analysis of the behavior of the models and guidelines for parameter tuning.

The recent and rapid deployment of CCTV cameras in public areas invokes the need for a capability to assist human operators in the real-time detection of threats and anomalous events. The main difficulty in this regard is the rare and unpredictable nature of the events to be detected. A typical strategy consists in modeling situations considered as normal and detecting outliers to this model. In this paper, we theoretically derive two variants of the hidden Markov model for proportional data modeling and assess their performance for unusual event detection in several public surveillance situations. Proportional data arise in a number of pattern recognition applications and classic hidden Markov models are not well adapted so far for their specific processing. Our models are based on the use of the generalized Dirichlet and Beta-Liouville distributions as emission probability functions and yield enhanced performance compared to the use of the Dirichlet distribution.