Anomaly Detection Using the Poisson Process Limit for Extremes

Anomaly detection starts from a model of normal behavior and classifies departures from this model as anomalies. This paper introduces a statistical non-parametric approach for anomaly detection that is based on a multivariate extension of the Poisson point process model for univariate extremes. The method is demonstrated on both a synthetic and a real-world data set, the latter being an unbalanced data set of acceleration data collected from movements of 7 pediatric patients suffering from epilepsy that is previously studied in [1]. The positive predictive values could be improved with an increase up to 12.9% (and a mean of 7%) while the sensitivity scores stayed unaltered. The proposed method was also shown to outperform an one-class SVM classifier. Because the Poisson point process model of extremes is able to combine information on the number of excesses over a fixed threshold with that on the excess values, a powerful model to detect anomalies is obtained that can be of high value in many applications.