{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-valid-optimal-assignment-kernels-and","title":"On Valid Optimal Assignment Kernels and Applications to Graph Classification","arxiv_id":"1606.01141","date":"2016-06-03","proceeding":"NeurIPS 2016 12","authors":["Nils M. Kriege","Pierre-Louis Giscard","Richard C. Wilson"],"abstract":"The success of kernel methods has initiated the design of novel positive\nsemidefinite functions, in particular for structured data. A leading design\nparadigm for this is the convolution kernel, which decomposes structured\nobjects into their parts and sums over all pairs of parts. Assignment kernels,\nin contrast, are obtained from an optimal bijection between parts, which can\nprovide a more valid notion of similarity. In general however, optimal\nassignments yield indefinite functions, which complicates their use in kernel\nmethods. We characterize a class of base kernels used to compare parts that\nguarantees positive semidefinite optimal assignment kernels. These base kernels\ngive rise to hierarchies from which the optimal assignment kernels are computed\nin linear time by histogram intersection. We apply these results by developing\nthe Weisfeiler-Lehman optimal assignment kernel for graphs. It provides high\nclassification accuracy on widely-used benchmark data sets improving over the\noriginal Weisfeiler-Lehman kernel.","url_abs":"http://arxiv.org/abs/1606.01141v3","url_pdf":"http://arxiv.org/pdf/1606.01141v3.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":[],"tasks":[{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"graph-classification","task_name":"Graph Classification"},{"task_slug":null,"task_name":"valid"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/graph-classification-on-mutag","task":"Graph Classification","dataset":"MUTAG","model":"WL-OA","rank_in_archive_order":64,"of":74,"metrics":{"Accuracy":"84.5%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-nci1","task":"Graph Classification","dataset":"NCI1","model":"WL-OA","rank_in_archive_order":6,"of":69,"metrics":{"Accuracy":"86.1%"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-nci109","task":"Graph Classification","dataset":"NCI109","model":"WL-OA","rank_in_archive_order":2,"of":38,"metrics":{"Accuracy":"86.3"},"uses_additional_data":false},{"leaderboard":"/sota/graph-classification-on-proteins","task":"Graph Classification","dataset":"PROTEINS","model":"WL-OA","rank_in_archive_order":48,"of":103,"metrics":{"Accuracy":"76.4%"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1606.01141","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}