Location recommendation is an important means to help people discover attractive locations. However, extreme sparsity of user-location matrices leads to a severe challenge, so it is necessary to take implicit feedback characteristics of user mobility data into account and leverage the location's spatial information. To this end, based on previously developed GeoMF, we propose a scalable and flexible framework, dubbed GeoMF++, for joint geographical modeling and implicit feedback-based matrix factorization. We then develop an efficient optimization algorithm for parameter learning, which scales linearly with data size and the total number of neighbor grids of all locations. GeoMF++ can be well explained from two perspectives. First, it subsumes two-dimensional kernel density estimation so that it captures spatial clustering phenomenon in user mobility data; Second, it is strongly connected with widely used neighbor additive models, graph Laplacian regularized models, and collective matrix factorization. Finally, we extensively evaluate GeoMF++ on two large-scale LBSN datasets. The experimental results show that GeoMF++ consistently outperforms the state-of-the-art and other competing baselines on both datasets in terms of NDCG and Recall. Besides, the efficiency studies show that GeoMF++ is much more scalable with the increase of data size and the dimension of latent space.
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