Incomplete Network Alignment: Problem Definitions and Fast Solutions

Networks are prevalent in many areas and are often collected from multiple sources. However, due to the veracity characteristics, more often than not, networks are incomplete. Network alignment and network completion have become two fundamental cornerstones behind a wealth of high-impact graph mining applications. The state-of-the-art have been addressing these two tasks in parallel. That is, most of the existing network alignment methods have implicitly assumed that the topology of the input networks for alignment are perfectly known a priori, whereas the existing network completion methods admit either a single network (i.e., matrix completion) or multiple aligned networks (e.g., tensor completion). In this article, we argue that network alignment and completion are inherently complementary with each other, and hence propose to jointly address them so that the two tasks can mutually benefit from each other. We formulate the problem from the optimization perspective, and propose an effective algorithm (iNeAt) to solve it. The proposed method offers two distinctive advantages. First (Alignment accuracy), our method benefits from the higher-quality input networks while mitigates the effect of the incorrectly inferred links introduced by the completion task itself. Second (Alignment efficiency), thanks to the low-rank structure of the complete networks and the alignment matrix, the alignment process can be significantly accelerated. We perform extensive experiments which show that (1) the network completion can significantly improve the alignment accuracy, i.e., up to 30% over the baseline methods; (2) the network alignment can in turn help recover more missing edges than the baseline methods; and (3) our method achieves a good balance between the running time and the accuracy, and scales with a provable linear complexity in both time and space.