Taxi services provide an urban transport option to citizens. Massive taxi trajectories contain rich information for understanding human travel activities, which are essential to sustainable urban mobility and transportation. The origin and destination (O-D) pairs of urban taxi trips can reveal the spatiotemporal patterns of human mobility and then offer fundamental information to interpret and reform formal, functional, and perceptual regions of cities. Matrices are one of the most effective models to represent taxi trajectories and O-D trips. Among matrix representations, non-negative matrix factorization (NMF) gives meaningful interpretations of complex latent relationships. However, the independence assumption for observations is violated by spatial and temporal autocorrelation in taxi flows, which is not compensated in classical NMF models. In order to discover human intra-urban mobility patterns, a novel spatiotemporal constraint NMF (STC-NMF) model that explicitly solves spatial and temporal dependencies is proposed in this paper. It factorizes taxi flow matrices in both spatial and temporal aspects, thus revealing inherent spatiotemporal patterns. With three-month taxi trajectories harvested in Beijing, China, the STC-NMF model is employed to investigate taxi travel patterns and their spatial interaction modes. As the results, four departure patterns, three arrival patterns, and eight spatial interaction patterns during weekdays and weekends are discovered. Moreover, it is found that intensive movements within certain time windows are significantly related to region functionalities and the spatial interaction flows exhibit an obvious distance decay tendency. The outcome of the proposed model is more consistent with the inherent spatiotemporal characteristics of human intra-urban movements. The knowledge gained in this research would be useful to taxi services and transportation management for promoting sustainable urban development.Sustainability 2019, 11, 4214 2 of 22 knowledge [6], including human mobility patterns [7,8], driving strategies of cabdrivers for seeking passengers [9][10][11][12], and urban spatial structures [13][14][15], for understanding human mobility and even improving sustainable urban transport.A taxi trip depends on the specific travel purpose. The origin and destination (O-D) points of a trip are considered the critical elements to represent mobility motions, while the route itself is less semantically representative for passengers. Generally, an O-D pair is exactly the pair of pick-up and drop-off points of a taxi ride, which represents the starting and stopping locations of a complete individual trip trajectory. O-D flows generalize not only trajectory geometries but also mobility semantics. Thus, previous studies have explored them to understand human mobility and urban structures. Direction and distance distributions of taxi trips were investigated to model the geographical heterogeneity and distance decay effect of intra-urban human mobility [8]. Mobility hotspots [16], movemen...