Where are the passengers?

Taxi bookings are events where requests for taxis are made by passengers either over voice calls or mobile apps. As the demand for taxis changes with space and time, it is important to model both the space and temporal dimensions in dynamic booking data. Several applications can benefit from a good taxi booking model. These include the prediction of number of bookings at certain location and time of the day, and the detection of anomalous booking events. In this paper, we propose a Grid-based Gaussian Mixture Model (GGMM) with spatio-temporal dimensions that groups booking data into a number of spatio-temporal clusters by observing the bookings occurring at different time of the day in each spatial grid cell. Using a large-scale real-world dataset consisting of over millions of booking records, we show that GGMM outperforms two strong baselines: a Gaussian Mixture Model (GMM) and the state-of-the-art spatio-temporal behavior model, Periodic Mobility Model (PMM), in estimating the spatio-temporal distribution of bookings at specific grid cells during specific time intervals. GGMM can achieve up to 95.8% (96.5%) reduction in perplexity compared against GMM (PMM). Further, we apply GGMM to detect anomalous bookings and successfully relate the anomalies with some known events, demonstrating GGMM's effectiveness in this task.