Graph embeddings have become a key paradigm to learn node representations and facilitate downstream graph analysis tasks. Many real-world scenarios such as online social networks and communication networks involve streaming graphs, where edges connecting nodes are continuously received in a streaming manner, making the underlying graph structures evolve over time. Such a streaming graph raises great challenges for graph embedding techniques not only in capturing the structural dynamics of the graph, but also in efficiently accommodating high-speed edge streams. Against this background, we propose SGSketch, a highly-efficient streaming graph embedding technique via incremental neighborhood sketching. SGSketch cannot only generate high-quality node embeddings from a streaming graph by gradually forgetting outdated streaming edges, but also efficiently update the generated node embeddings via an incremental embedding updating mechanism. Our extensive evaluation compares SGSketch against a sizable collection of state-of-the-art techniques using both synthetic and real-world streaming graphs. The results show that SGSketch achieves superior performance on different graph analysis tasks, showing 31.9% and 21.9% improvement on average over the best-performing static and dynamic graph embedding baselines, respectively. Moreover, SGSketch is significantly more efficient in both embedding learning and incremental embedding updating processes, showing 54x-1813x and 118x-1955x speedup over the baseline techniques, respectively.

Location-Based Social Networks (LBSNs) have been widely used as a primary data source for studying 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. Against this background, we propose in this paper LBSN2Vec++, a heterogeneous hypergraph embedding approach designed specifically for LBSN data for automatic feature learning. Specifically, LBSN data intrinsically forms a heterogeneous hypergraph including both user-user homogeneous edges (friendships) and user-time-POI-semantic heterogeneous 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 not only preserving the nn-wise node proximity captured by the hyperedges, but also considering embedding space transformation between node domains to fully grasp the complex structural characteristics of the LBSN heterogeneous hypergraph. Using real-world LBSN datasets collected in six cities all over the world, our extensive evaluation shows that LBSN2Vec++ significantly and consistently outperforms both state-of-the-art graph embedding techniques by up to 68 percent and the best-performing hand-crafted features in the literature by up to 70.14 percent on friendship and location prediction tasks.