{"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/the-multiscale-laplacian-graph-kernel","title":"The Multiscale Laplacian Graph Kernel","arxiv_id":"1603.06186","date":"2016-03-20","proceeding":"NeurIPS 2016 12","authors":["Risi Kondor","Horace Pan"],"abstract":"Many real world graphs, such as the graphs of molecules, exhibit structure at\nmultiple different scales, but most existing kernels between graphs are either\npurely local or purely global in character. In contrast, by building a\nhierarchy of nested subgraphs, the Multiscale Laplacian Graph kernels (MLG\nkernels) that we define in this paper can account for structure at a range of\ndifferent scales. At the heart of the MLG construction is another new graph\nkernel, called the Feature Space Laplacian Graph kernel (FLG kernel), which has\nthe property that it can lift a base kernel defined on the vertices of two\ngraphs to a kernel between the graphs. The MLG kernel applies such FLG kernels\nto subgraphs recursively. To make the MLG kernel computationally feasible, we\nalso introduce a randomized projection procedure, similar to the Nystr\\\"om\nmethod, but for RKHS operators.","url_abs":"http://arxiv.org/abs/1603.06186v2","url_pdf":"http://arxiv.org/pdf/1603.06186v2.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":"graph-classification","task_name":"Graph Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/graph-classification-on-proteins","task":"Graph Classification","dataset":"PROTEINS","model":"MLG","rank_in_archive_order":49,"of":103,"metrics":{"Accuracy":"76.34%"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1603.06186","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}