Wasserstein Embedding for Graph Learning

Soheil Kolouri, Navid Naderializadeh, Gustavo K. Rohde, Heiko Hoffmann

Keywords: Wasserstein, graph embedding, graph-level prediction

Abstract: We present Wasserstein Embedding for Graph Learning (WEGL), a novel and fast framework for embedding entire graphs in a vector space, in which various machine learning models are applicable for graph-level prediction tasks. We leverage new insights on defining similarity between graphs as a function of the similarity between their node embedding distributions. Specifically, we use the Wasserstein distance to measure the dissimilarity between node embeddings of different graphs. Unlike prior work, we avoid pairwise calculation of distances between graphs and reduce the computational complexity from quadratic to linear in the number of graphs. WEGL calculates Monge maps from a reference distribution to each node embedding and, based on these maps, creates a fixed-sized vector representation of the graph. We evaluate our new graph embedding approach on various benchmark graph-property prediction tasks, showing state-of-the-art classification performance while having superior computational efficiency. The code is available at https://github.com/navid-naderi/WEGL.

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One-sentence Summary: Wasserstein Embedding for Graph Learning (WEGL) is a novel and fast framework for embedding entire graphs into a vector space in which the Euclidean distance between representations approximates the 2-Wasserstein distance.

Code: [ navid-naderi/WEGL](https://github.com/navid-naderi/WEGL)

Data: [COLLAB](https://paperswithcode.com/dataset/collab), [ENZYMES](https://paperswithcode.com/dataset/enzymes), [IMDB-BINARY](https://paperswithcode.com/dataset/imdb-binary), [IMDB-MULTI](https://paperswithcode.com/dataset/imdb-multi), [MUTAG](https://paperswithcode.com/dataset/mutag), [NCI1](https://paperswithcode.com/dataset/nci1), [OGB](https://paperswithcode.com/dataset/ogb), [Open Graph Benchmark](https://paperswithcode.com/dataset/open-graph-benchmark), [PROTEINS](https://paperswithcode.com/dataset/proteins), [PTC](https://paperswithcode.com/dataset/ptc), [REDDIT-5K](https://paperswithcode.com/dataset/reddit-5k), [REDDIT-BINARY](https://paperswithcode.com/dataset/reddit-binary), [Reddit](https://paperswithcode.com/dataset/reddit)

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2006.09430/code)