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Compared with traditional Gromov-Wasserstein and semi-relaxed variants, DsrFGW addresses sparse, noisy, or partially observed graphs by incorporating diffusion to model information propagation. Experiments on 36 synthetic pairwise graph matching tasks show consistent gains over srFGW, including improved internal and external clustering quality (ARI and accuracy), robustness under severe noise, and diffusion scales adapting to problem difficulty.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/diffusion-enabled-optimal-transport-distances-for-graph-matching-paper/328144/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/diffusion-enabled-optimal-transport-distances-for-graph-matching-paper/328144.png","ImageObject",300,407,{"name":92,"@type":93},"Theodora","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-09","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does DsrFGW address in graph matching?","Question",{"text":112,"@type":113},"It targets graph comparison under structural uncertainty, especially for sparse, noisy, or partially observed graphs where traditional OT-based distances and semi-relaxed variants can struggle.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does diffusion improve the DsrFGW framework?",{"text":117,"@type":113},"DsrFGW diffuses node attributes before computing the transport plan, enabling information propagation across nodes so that both local and global structural patterns are captured and noise sensitivity is reduced.",{"name":119,"@type":110,"acceptedAnswer":120},"What evidence supports the performance of DsrFGW?",{"text":121,"@type":113},"Across 36 synthetic pairwise graph matching tasks of varying difficulty, DsrFGW shows consistent superiority over srFGW, with accuracy improvements and large Adjusted Rand Index gains, including better clustering quality in most noisy scenarios.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},328144,1791404931,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":36,"preview_page_count":4},687197207919,"https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552","Diffusion-enabled Optimal Transport distances for graph  \nmatching  \nIman Seyedi 1[0000-0003-1875-7565] and Francesco Archetti 1[0000-0003-1131-3830]  \n1 Department of Computer Science Systems and Communication, University of Milano-Bi  \ncocca, 20126 Milan, Italy  \n[seyediman.seyedi@unimib.it](seyediman.seyedi@unimib.it) [francesco.archetti@unimib.it](francesco.archetti@unimib.it)  \n[Abstract](Abstract). This paper introduces Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW), a novel method for graph comparison that unifies node features and structural connectivity through optimal transport. While traditional Gromov-Wasserstein and semi-relaxed variants (srGW, srFGW) capture graph structure, they often struggle with sparse, noisy, or partially observed graphs. Inspired by Graph Diffusion Distance—which posits graphs are similar if they enable similar information transmission patterns—DsrFGW incorporates diffusion processes allowing information propagation across nodes, capturing local and global structural patterns while reducing sensitivity to noise or missing edges. An extensive evaluation on 36 synthetic pairwise graph matching tasks (easy, medium, hard) demonstrates consistent superiority over srFGW, achieving accuracy improvements of 0-20 percentage points and dramatic Adjusted Rand Index (ARI) gains: in medium-difficulty scenarios, srFGW often achieves negative ARI (worse than random) while DsrFGW offers better performance in terms of both internal and external clustering quality measures (i.e., Adjusted Rank Index and Accuracy with respect to the true underlying clusters, respectively) . Even under severe noise, DsrFGW improves clustering quality in 92% of the synthetic tasks with optimal diffusion scales adapting to problem difficulty, establishing DsrFGW as a robust framework for graph comparison under structural uncertainty.  \nKeywords: Optimal Transport, Graph Diffusion, Semi-Relaxed Gromov-Wasserstein, Graph Matching, Metric Measure Spaces  \n1 Introduction  \nGraph-structured data arises naturally in many domains, including neuroscience, social networks, and transportation systems. Nodes carry descriptive features while edges encode structural relationships, making graph comparison central to machine learning and network analysis. Traditional supervised alignment methods, relying on predefined correspondences, often fail with noisy, sparsely connected, or partially observed networks. Optimal Transport (OT) provides a principled framework for comparing probability measures, while its extension—Gromov-Wasserstein (GW) distances—enables graph comparison based on structure alone, without requiring direct node-to-node correspondences. Semi-relaxed variants (srGW, srFGW) further improve computational  \nefficiency and allow incorporation of node features through fused formulations [1], successfully applied to unsupervised alignment of brain connectivity networks [2] and other node-attributed graphs.  \nGraph Diffusion Distance (GDD) measures graph similarity by comparing information propagation across networks [3], [4] . Diffusion distances capture local and global structural patterns, are robust to edge deletions, and complement OT-based methods by emphasizing graph dynamics rather than static connectivity alone. The core intuition is that node features should incorporate information from their neighborhood through the graph structure. Figure 1 illustrates this process: starting from localized feature values (τ = 0), the heat kernel diffusion operator gradually propagates information along graph edges. At small diffusion parameter (τ = 0.05), features spread to immediate neighbors, while larger diffusion (τ = 0.5) induces global smoothing that captures multi-hop structural relationships, effectively enriching feature representation by encoding graph topology directly into node attributes.  \nFig. 1. Heat kernel diffusion on graphs. Initially (τ = 0), three nodes have distinct feature values (red +1.0, blue-1.0, light","cbCaiqhE4X8atSVj","https://ap.wps.com/l/cbCaiqhE4X8atSVj","pdf",790779,16,"English","# 1 Introduction\n## 2 Related Works\n# 3 Mathematical Background\n# 4 DsrFGW Algorithm\n# 5 Numerical Experiments\n# 6 Conclusions and Future Perspectives","[{\"question\":\"What problem does DsrFGW address in graph matching?\",\"answer\":\"It targets graph comparison under structural uncertainty, especially for sparse, noisy, or partially observed graphs where traditional OT-based distances and semi-relaxed variants can struggle.\"},{\"question\":\"How does diffusion improve the DsrFGW framework?\",\"answer\":\"DsrFGW diffuses node attributes before computing the transport plan, enabling information propagation across nodes so that both local and global structural patterns are captured and noise sensitivity is reduced.\"},{\"question\":\"What evidence supports the performance of DsrFGW?\",\"answer\":\"Across 36 synthetic pairwise graph matching tasks of varying difficulty, DsrFGW shows consistent superiority over srFGW, with accuracy improvements and large Adjusted Rand Index gains, including better clustering quality in most noisy scenarios.\"}]","Diffusion-enabled Optimal Transport distances for graph matching - Paper | PDF",1789978738]