The prevalence of location-based social networks (LBSNs) has eased the understanding of human mobility patterns. Knowledge of human dynamics can aid in various ways like urban planning, managing traffic congestion, personalized recommendation etc. These dynamics are influenced by factors like social impact, periodicity in mobility, spatial proximity, influence among users and semantic categories etc., which makes location modelling a critical task. However, categories which act as semantic characterization of the location, might be missing for some check-ins and can adversely affect modelling the mobility dynamics of users. At the same time, mobility patterns provide a cue on the missing semantic category. In this paper, we simultaneously address the problem of semantic annotation of locations and location adoption dynamics of users. We propose our model HAP-SAP, a latent spatio-temporal multivariate Hawkes process, which considers latent semantic category influences, and temporal and spatial mobility patterns of users. The model parameters and latent semantic categories are inferred using expectation-maximization algorithm, which uses Gibbs sampling to obtain posterior distribution over latent semantic categories. The inferred semantic categories can supplement our model on predicting the next check-in events by users. Our experiments on real datasets demonstrate the effectiveness of the proposed model for the semantic annotation and location adoption modelling tasks.
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