{"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/fast-online-node-labeling-for-very-large","title":"Fast Online Node Labeling for Very Large Graphs","arxiv_id":"2305.16257","date":"2023-05-25","proceeding":null,"authors":["Baojian Zhou","Yifan Sun","Reza Babanezhad"],"abstract":"This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with $\\mathcal{O}(n^3)$ runtime and $\\mathcal{O}(n^2)$ space complexity or sample a large volume of random spanning trees, thus are difficult to scale to large graphs. In this work, we propose an improvement based on the \\textit{online relaxation} technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret $\\mathcal{O}(\\sqrt{n^{1+\\gamma}})$ when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying $\\mathcal{O}(k\\sqrt{n^{1+\\gamma}})$ regret based on this relaxation. The key of FastONL is a \\textit{generalized local push} method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is $\\mathcal{O}(\\text{vol}({\\mathcal{S}})\\log 1/\\epsilon)$ locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.","url_abs":"https://arxiv.org/abs/2305.16257v2","url_pdf":"https://arxiv.org/pdf/2305.16257v2.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":"fast-online-node-labeling-for-very-large","repo_url":"https://github.com/baojian/FastONL","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"node-classification","task_name":"Node Classification"},{"task_slug":"transductive-learning","task_name":"Transductive Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2305.16257","atlas_url":"https://app.syntology.ai/?focus=2305.16257","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2305.16257"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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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