Low rank methods for multiple network alignment
This addresses the computational bottleneck in aligning multiple networks for researchers and practitioners in fields like bioinformatics or social network analysis, offering a scalable solution where prior methods fail, though it is an incremental improvement based on extending pairwise techniques.
The paper tackles the problem of multiple network alignment, where existing methods scale poorly with the number of networks, by introducing a new algorithm that leverages low-rank tensor structures to align thousands of networks with thousands of nodes efficiently, showing it matches or outperforms existing methods in quality while running faster and scaling to previously unreachable problem sizes.
Multiple network alignment is the problem of identifying similar and related regions in a given set of networks. While there are a large number of effective techniques for pairwise problems with two networks that scale in terms of edges, these cannot be readily extended to align multiple networks as the computational complexity will tend to grow exponentially with the number of networks.In this paper we introduce a new multiple network alignment algorithm and framework that is effective at aligning thousands of networks with thousands of nodes. The key enabling technique of our algorithm is identifying an exact and easy to compute low-rank tensor structure inside of a principled heuristic procedure for pairwise network alignment called IsoRank. This can be combined with a new algorithm for $k$-dimensional matching problems on low-rank tensors to produce the alignment. We demonstrate results on synthetic and real-world problems that show our technique (i) is as good or better in terms of quality as existing methods, when they work on small problems, while running considerably faster and (ii) is able to scale to aligning a number of networks unreachable by current methods. We show in this paper that our method is the realistic choice for aligning multiple networks when no prior information is present.