WL-Align: Weisfeiler-Lehman Relabeling for Aligning Users Across Networks via Regularized Representation Learning

Aligning users across networks using graph representation learning has been found effective where the alignment is accomplished in a low-dimensional embedding space. Yet, highly precise alignment remains challenging, especially for nodes with long-range connectivity to labeled anchors. To alleviate this limitation, we propose WL-Align which employs a regularized representation learning framework to learn distinctive node representations. It extends the Weisfeiler-Lehman Isormorphism Test and learns the alignment in alternating phases of 'across-network Weisfeiler-Lehman relabeling' and 'proximity-preserving representation learning'. The across-network Weisfeiler-Lehman relabeling is achieved through iterating the anchor-based label propagation and a similarity-based hashing to exploit the known anchors' connectivity to different nodes in an efficient and robust manner. The representation learning module preserves the second-order proximity within individual networks and is regularized by the across-network Weisfeiler-Lehman hash labels. Extensive experiments on real-world and synthetic datasets have demonstrated that our proposed WL-Align outperforms the state-of-the-art methods, achieving significant performance improvements in the 'exact matching' scenario.