Online common change-point detection in a set of nonstationary categorical time series

Abstract

Categorical sequences are widely used in various domains to describe the evolutionary state of the process under study. This article addresses the problem of behavioral change detection for multiple categorical time series. Relying on the sequential likelihood ratio test, an online change detection method is proposed based on the joint modeling of all the categorical sequences. To model the joint probability density, a nonhomogeneous Markov model is used. It allows modeling the transition dynamics over time and considering their dependence on some exogenous factors that may influence the behavior changes. An adaptive threshold is learned using Monte Carlo simulations to detect different changes and reduce false alarms. The performance of the proposed method is evaluated using two real-world and four synthetic datasets. It is compared with two state-of-the-art change detection methods, namely logistic regression and homogeneous Markov model. The experimentation using synthetic datasets highlights the proposed method’s effectiveness in terms of both the detection precision and the detection delay. The real-world data are issued from a water network and school-to-work transition. The analysis of the model estimated parameters allows us to characterize the detected changes in a real-world context.