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Wasserstein Embedding for Graph Learning

16 Jun 2020ICLR 2021 1arXiv:2006.09430archive 2025-07-28

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

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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Code

navid-naderi/WEGL officialmentioned in papermentioned on GitHubpytorch report

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Tasks

Computational EfficiencyGraph ClassificationGraph EmbeddingGraph LearningGraph Property PredictionProperty Prediction

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Graph Classification COLLAB WEGL Accuracy 79.8% #14 of 39 Archive leaderboard report
Graph Classification D&D WEGL Accuracy 78.6% #27 of 53 Archive leaderboard report
Graph Classification ENZYMES WEGL Accuracy 60.5 #28 of 54 Archive leaderboard report
Graph Classification IMDb-B WEGL Accuracy 75.4% #23 of 51 Archive leaderboard report
Graph Classification IMDb-M WEGL Accuracy 52% #12 of 36 Archive leaderboard report
Graph Classification MUTAG WEGL Accuracy 88.3% #41 of 74 Archive leaderboard report
Graph Classification NCI1 WEGL Accuracy 76.8% #45 of 69 Archive leaderboard report
Graph Classification PROTEINS WEGL Accuracy 76.5% #43 of 103 Archive leaderboard report
Graph Classification PTC WEGL Accuracy 67.5% #17 of 37 Archive leaderboard report
Graph Classification RE-M12K WEGL Accuracy 47.8% #4 of 6 Archive leaderboard report
Graph Classification RE-M5K WEGL Accuracy 55.1% #3 of 8 Archive leaderboard report
Graph Classification REDDIT-B WEGL Accuracy 92 #5 of 12 Archive leaderboard report
Graph Property Prediction ogbg-molhiv WEGL Ext. data No #34 of 43 Archive leaderboard report
Graph Property Prediction ogbg-molhiv WEGL Number of params 361064 #34 of 43 Archive leaderboard report
Graph Property Prediction ogbg-molhiv WEGL Test ROC-AUC 0.7757 ± 0.0111 #34 of 43 Archive leaderboard report
Graph Property Prediction ogbg-molhiv WEGL Validation ROC-AUC 0.8101 ± 0.0097 #34 of 43 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

Introduced by this paper: WEGL

WEGL

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