COPT: Coordinated Optimal Transport for Graph Sketching
This provides an unsupervised method for graph representation, addressing graph sketching and comparison tasks, with incremental improvements in classification performance.
The paper tackled the problem of measuring distances between graphs by introducing COPT, a novel metric based on coordinated optimal transport, which outperformed state-of-the-art methods in graph classification on synthetic and real datasets.
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.