Papers › Optimal Transport for structured data with application on graphs
Optimal Transport for structured data with application on graphs
Titouan Vayer, Laetitia Chapel, Rémi Flamary, Romain Tavenard, Nicolas Courty
This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a total cost of transporting probability masses) that unveils the geometric nature of the structured objects space. Unlike Wasserstein or Gromov-Wasserstein metrics that focus solely and respectively on features (by considering a metric in the feature space) or structure (by seeing structure as a metric space), our new distance exploits jointly both information, and is consequently called Fused Gromov-Wasserstein (FGW). After discussing its properties and computational aspects, we show results on a graph classification task, where our method outperforms both graph kernels and deep graph convolutional networks. Exploiting further on the metric properties of FGW, interesting geometric objects such as Fr\'echet means or barycenters of graphs are illustrated and discussed in a clustering context.
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Code
Syntology Ran 3 of 3 code samples harvested from 1 repository linked to this paper; 0 have no recorded run. Of those that ran: 1 ran · honoured contract; 1 ran · violated contract; 1 ran · fixture could not drive it.
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Code Syntology ran Syntology
3 samples harvested; 3 ran; 1 honoured the contract we drafted; 0 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Graph Classification | ENZYMES | FGW sp | Accuracy | 71.00% | #11 of 54 | Archive leaderboard | report |
| Graph Classification | MUTAG | FGW wl h=4 sp | Accuracy | 88.42% | #38 of 74 | Archive leaderboard | report |
| Graph Classification | MUTAG | FGW wl h=2 sp | Accuracy | 86.42% | #55 of 74 | Archive leaderboard | report |
| Graph Classification | MUTAG | FGW raw sp | Accuracy | 83.26% | #69 of 74 | Archive leaderboard | report |
| Graph Classification | NCI1 | FGW wl h=4 sp | Accuracy | 86.42% | #4 of 69 | Archive leaderboard | report |
| Graph Classification | NCI1 | FGW wl h=2 sp | Accuracy | 85.82% | #7 of 69 | Archive leaderboard | report |
| Graph Classification | NCI1 | FGW raw sp | Accuracy | 72.82% | #59 of 69 | Archive leaderboard | report |
| Graph Classification | PROTEINS | FGW sp | Accuracy | 74.55% | #79 of 103 | 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.
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