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Detection of anomalous behaviour using mixtures of von Mises distributions and an extension of the CUSUM algorithm

The detection of anomalies in the daily behaviour of a monitored person is of crucial interest to discover degenerative diseases, medication changes or any important problem in the health of… Click to show full abstract

The detection of anomalies in the daily behaviour of a monitored person is of crucial interest to discover degenerative diseases, medication changes or any important problem in the health of the monitored person. In this work we focus on the detection of anomalies in the transit between the different rooms of his/her house. For this purpose, we propose to model the transit times using a mixture of von Mises distributions and estimate the parameters using the EM algorithm. An extension of the CUSUM algorithm is proposed to detect changes. This extension is based on reformulating this algorithm as a hypothesis test on the model parameters, using the likelihood ratio. In order to verify the validity of the method, extensive experimentation has been performed.

Keywords: detection; mises distributions; von mises; detection anomalous; extension cusum; cusum algorithm

Journal Title: Journal of Statistical Computation and Simulation
Year Published: 2025

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