Just SLaQ When You Approximate: Accurate Spectral Distances for Web-Scale Graphs
This addresses the scalability challenge in graph comparison for data mining and information retrieval, offering a significant improvement over previous methods.
The paper tackles the problem of efficiently computing spectral distances for large graphs, proposing SLaQ, which achieves accurate approximations in linear time relative to edges, outperforming existing methods by orders of magnitude in accuracy and enabling comparisons of million-scale graphs in minutes on a single machine.
Graph comparison is a fundamental operation in data mining and information retrieval. Due to the combinatorial nature of graphs, it is hard to balance the expressiveness of the similarity measure and its scalability. Spectral analysis provides quintessential tools for studying the multi-scale structure of graphs and is a well-suited foundation for reasoning about differences between graphs. However, computing full spectrum of large graphs is computationally prohibitive; thus, spectral graph comparison methods often rely on rough approximation techniques with weak error guarantees. In this work, we propose SLaQ, an efficient and effective approximation technique for computing spectral distances between graphs with billions of nodes and edges. We derive the corresponding error bounds and demonstrate that accurate computation is possible in time linear in the number of graph edges. In a thorough experimental evaluation, we show that SLaQ outperforms existing methods, oftentimes by several orders of magnitude in approximation accuracy, and maintains comparable performance, allowing to compare million-scale graphs in a matter of minutes on a single machine.