Scalable gromov-wasserstein learning for graph partitioning and matching
We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on graphs. Given two graphs, the optimal transport associated with their Gromov-Wasserstein discrepancy provides the correspondence between their nodes and achieves graph matching. When one of the graphs has isolated but self-connected nodes (i.e., a disconnected graph), the optimal transport indicates the clustering structure of the other graph and achieves graph partitioning. Using this concept, we extend our method to multi-graph partitioning and matching by learning a Gromov-Wasserstein barycenter graph for multiple observed graphs; the barycenter graph plays the role of the disconnected graph, and since it is learned, so is the clustering. Our method combines a recursive K-partition mechanism with a regularized proximal gradient algorithm, whose time complexity is O(K(E + V ) logK V ) for graphs with V nodes and E edges. To our knowledge, our method is the first attempt to make Gromov-Wasserstein discrepancy applicable to large-scale graph analysis and unify graph partitioning and matching into the same framework. It outperforms state-of-the-art graph partitioning and matching methods, achieving a trade-off between accuracy and efficiency.
Duke Scholars
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- 4611 Machine learning
- 1702 Cognitive Sciences
- 1701 Psychology
Citation
Published In
ISSN
Publication Date
Volume
Related Subject Headings
- 4611 Machine learning
- 1702 Cognitive Sciences
- 1701 Psychology