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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.","url_abs":"https://arxiv.org/abs/1805.09114v3","url_pdf":"https://arxiv.org/pdf/1805.09114v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"optimal-transport-for-structured-data-with","repo_url":"https://github.com/tvayer/FGW","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"optimal-transport-for-structured-data-with","repo_url":"https://github.com/rflamary/POT","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"graph-classification","task_name":"Graph Classification"},{"task_slug":"graph-clustering","task_name":"Graph Clustering"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/graph-classification-on-enzymes","task":"Graph Classification","dataset":"ENZYMES","model":"FGW sp","rank_in_archive_order":11,"of":54,"metrics":{"Accuracy":"71.00%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-mutag","task":"Graph Classification","dataset":"MUTAG","model":"FGW wl h=4 sp","rank_in_archive_order":38,"of":74,"metrics":{"Accuracy":"88.42%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-mutag","task":"Graph Classification","dataset":"MUTAG","model":"FGW wl h=2 sp","rank_in_archive_order":55,"of":74,"metrics":{"Accuracy":"86.42%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-mutag","task":"Graph Classification","dataset":"MUTAG","model":"FGW raw sp","rank_in_archive_order":69,"of":74,"metrics":{"Accuracy":"83.26%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-nci1","task":"Graph Classification","dataset":"NCI1","model":"FGW wl h=4 sp","rank_in_archive_order":4,"of":69,"metrics":{"Accuracy":"86.42%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-nci1","task":"Graph Classification","dataset":"NCI1","model":"FGW wl h=2 sp","rank_in_archive_order":7,"of":69,"metrics":{"Accuracy":"85.82%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-nci1","task":"Graph Classification","dataset":"NCI1","model":"FGW raw sp","rank_in_archive_order":59,"of":69,"metrics":{"Accuracy":"72.82%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-proteins","task":"Graph Classification","dataset":"PROTEINS","model":"FGW sp","rank_in_archive_order":79,"of":103,"metrics":{"Accuracy":"74.55%"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1805.09114","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1805.09114"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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