Network alignment is the problem of pairing nodes between two graphs such that the paired nodes are structurally and semantically similar. A well-known application of network alignment is to identify which accounts in different social networks belong to the same person. Existing alignment techniques, however, lack scalability, cannot incorporate multi-dimensional information without training data, and are limited in the consistency constraints enforced by an alignment. In this paper, we propose a fully unsupervised network alignment framework based on a multi-order embedding model. The model learns the embeddings of each node using a graph convolutional neural representation, which we prove to satisfy consistency constraints. We further design a data augmentation method and a refinement mechanism to make the model adaptive to consistency violations and noise. Extensive experiments on real and synthetic datasets show that our model outperforms state-of-the-art alignment techniques. We also demonstrate the robustness of our model against adversarial conditions, such as structural noises, attribute noises, graph size imbalance, and hyper-parameter sensitivity.

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Location-based social networks (LBSNs) have emerged over the past few years. Their exponential network effects depend on the fact that each user can share her daily digital footprints with different communities, in different places, and at different times (for example in the form of check-in activities). Unlike other types of social networks, activities in an LBSN can potentially be performed by several users in a collaborative way. Existing studies of representation learning for LBSNs often consider them as regular graphs and ignore these high-order, dynamic, and multi-role contexts, since their holistic interactions are quite difficult to capture. In this paper, we propose a model in which these holistic interactions can be learned and transferred into node embeddings derived from a hypergraph representation and a persona decomposition process. More specifically, the model learns from friendship edges, check-in hyperedges, and node personas at the same time, and devises multiple presentations for each user that reflects their multiple roles in a social context. The embedding learning process also exploits useful patterns such as user colocation and sequential effects through a carefully designed point-of-interest splitting step. Extensive experiments on real and synthetic datasets show that our model outperforms alternative state-of-the-art embedding methods on friendship and location prediction tasks by an average margin of 45.7% and 29.46%, respectively. We also demonstrate the robustness of our model against adversarial conditions such as structural noise, attribute noise, and hyperparameter sensitivity.