Dynamic modeling and online monitoring of tensor data streams with application to passenger flow surveillance

Abstract

Passenger flow surveillance in urban transport systems has emerged as a major global issue for smart city management. Governments are taking proper measures to monitor passenger flow in order to maintain social stability and to prevent unexpected group events. It is critical to develop a passenger flow surveillance system that continuously monitors the passenger flow over time and triggers a signal as soon as the passenger flow begins to deteriorate so that timely government intervention can be implemented. In this paper passenger flow surveillance is novelly formulated as dynamic modeling and online monitoring of tensor data streams. Existing tensor monitoring methods either rely heavily on the assumption that the tensor coefficients exhibit a low-rank structure or are inapplicable to general-order tensors. We propose a unified monitoring framework based on the tensor normal distribution to overcome these challenges. We begin by developing a tensor model selection procedure that ensures that the chosen tensor structure strikes a balance between model complexity and estimation accuracy. Then we propose an online estimation procedure to dynamically estimate the tensor parameters on which sequential change-detection procedures, using the generalized likelihood ratio test, are proposed. Extensive simulations and an analysis of real passenger flow data in Hong Kong demonstrate the efficacy of our approach.