Detecting Geographical Competitive Structure for POI Visit Dynamics

We provide a framework for analyzing geographical influence networks that have impacts on visit event sequences for a set of point-of-interests (POIs) in a city. Since mutually-exciting Hawkes processes can naturally model temporal event data and capture interactions between those events, previous work presented a probabilistic model based on Hawkes processes, called CHP model, for finding cooperative structure among online items from their share event sequences. In this paper, based on Hawkes processes, we propose a novel probabilistic model, called RH model, for detecting geographical competitive structure in the set of POIs, and present a method of inferring it from the POI visit event history. We mathematically derive an analytical approximation formula for predicting the popularity of each of the POIs for the RH model, and also extend the CHP model so as to extract geographical cooperative structure. Using synthetic data, we first confirm the effectiveness of the inference method and the validity of the approximation formula. Using real data of Location-Based Social Networks (LBSNs), we demonstrate the significance of the RH model in terms of predicting the future events, and uncover the latent geographical influence networks from the perspective of geographical competitive and cooperative structures.