COPT: Coordinated Optimal Transport for Graph Sketching

• URL: http://arxiv.org/abs/2003.03892v2
• Date: Mon, 15 Jun 2020 18:21:17 GMT
• Title: COPT: Coordinated Optimal Transport for Graph Sketching
• Abstract summary: COPT is a novel distance metric between graphs defined via an optimization routine. We show theoretically that our method preserves important global structural information on graphs. Empirically, COPT outperforms state of the art methods in graph classification on both synthetic and real datasets.
• Score: 15.127728811011245
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an unsupervised way to learn general-purpose graph representation, applicable to both graph sketching and graph comparison. COPT involves simultaneously optimizing dual transport plans, one between the vertices of two graphs, and another between graph signal probability distributions. We show theoretically that our method preserves important global structural information on graphs, in particular spectral information, and analyze connections to existing studies. Empirically, COPT outperforms state of the art methods in graph classification on both synthetic and real datasets.

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