Will Sawin

Yihe Dong, Will Sawin, Yoshua Bengio

Hypergraphs provide a natural representation for many real world datasets. We propose a novel framework, HNHN, for hypergraph representation learning. HNHN is a hypergraph convolution network with nonlinear activation functions applied to both hypernodes and hyperedges, combined with a normalization scheme that can flexibly adjust the importance of high-cardinality hyperedges and high-degree vertices depending on the dataset. We demonstrate improved performance of HNHN in both classification accuracy and speed on real world datasets when compared to state of the art methods.

Yihe Dong, Will Sawin

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.