Point-of-Interest (POI) recommendation has become an important means to help people discover attractive and interesting places, especially when users travel out of town. However, the extreme sparsity of a user-POI matrix creates a severe challenge. To cope with this challenge, we propose a unified probabilistic generative model, the Topic-Region Model (TRM), to simultaneously discover the semantic, temporal, and spatial patterns of users' check-in activities, and to model their joint effect on users' decision making for selection of POIs to visit. To demonstrate the applicability and flexibility of TRM, we investigate how it supports two recommendation scenarios in a unified way, that is, hometown recommendation and out-of- town recommendation. TRM effectively overcomes data sparsity by the complementarity and mutual enhancement of the diverse information associated with users' check-in activities (e.g., check-in content, time, and location) in the processes of discovering heterogeneous patterns and producing recommendations. To support real-time POI recommendations, we further extend the TRM model to an online learning model, TRM-Online, to track changing user interests and speed up the model training. In addition, based on the learned model, we propose a clustering-based branch and bound algorithm (CBB) to prune the POI search space and facilitate fast retrieval of the top-k recommendations. We conduct extensive experiments to evaluate the performance of our proposals on two real-world datasets, including recommendation effectiveness, overcoming the cold-start problem, recommendation efficiency, and model-training efficiency. The experimental results demonstrate the superiority of our TRM models, especially TRM-Online, compared with state-of-the-art competitive methods, by making more effective and efficient mobile recommendations. In addition, we study the importance of each type of pattern in the two recommendation scenarios, respectively, and find that exploiting temporal patterns is most important for the hometown recommendation scenario, while the semantic patterns play a dominant role in improving the recommendation effectiveness for out-of-town users.
