Location Based Social Networks (LBSNs) have been widely used as a primary data source to study the impact of mobility and social relationships on each other. Traditional approaches manually define features to characterize users' mobility homophily and social proximity, and show that mobility and social features can help friendship and location prediction tasks, respectively. However, these hand-crafted features not only require tedious human efforts, but also are difficult to generalize. In this paper, by revisiting user mobility and social relationships based on a large-scale LBSN dataset collected over a long-term period, we propose LBSN2Vec, a hypergraph embedding approach designed specifically for LBSN data for automatic feature learning. Specifically, LBSN data intrinsically forms a hypergraph including both user-user edges (friendships) and user-time-POI-semantic hyperedges (check-ins). Based on this hypergraph, we first propose a random-walk-with-stay scheme to jointly sample user check-ins and social relationships, and then learn node embeddings from the sampled (hyper)edges by preserving n-wise node proximity (n = 2 or 4). Our evaluation results show that LBSN2Vec both consistently and significantly outperforms the state-of-the-art graph embedding methods on both friendship and location prediction tasks, with an average improvement of 32.95% and 25.32%, respectively. Moreover, using LBSN2Vec, we discover the asymmetric impact of mobility and social relationships on predicting each other, which can serve as guidelines for future research on friendship and location prediction in LBSNs.
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