Hidden Markov Flow Network Model: A Generative Model for Dynamic Flow on a Network

Abstract

In this paper, we propose a generative model that describes the dynamics of flow on a network-the hidden Markov flow network (HMFN) model, which is inspired by the gravity model in traffic engineering. Each node in the network has a dynamic hidden state and the flow observed on links depends on the states of the nodes being connected. For model inference, a collapsed Gibbs sampling algorithm is also proposed. Lastly, the model is applied to synthetic data and real human mobility network generated by GPS data from taxis in Bangkok. The synthetic data example shows that the reconstruction accuracy of the proposed method outperforms compared with the k-means method and the hidden Markov model, which do not consider the network interaction. The results of human mobility data show that the HMFN model can be used for spatio-temporal anomaly detection and prediction of future flow patterns. Index Terms-Generative model, dynamics of flow network, bayesian inference, spatio-temporal pattern mining.