{"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/sublinear-time-clustering-oracle-for-signed","title":"Sublinear-Time Clustering Oracle for Signed Graphs","arxiv_id":"2206.13813","date":"2022-06-28","proceeding":null,"authors":["Stefan Neumann","Pan Peng"],"abstract":"Social networks are often modeled using signed graphs, where vertices correspond to users and edges have a sign that indicates whether an interaction between users was positive or negative. The arising signed graphs typically contain a clear community structure in the sense that the graph can be partitioned into a small number of polarized communities, each defining a sparse cut and indivisible into smaller polarized sub-communities. We provide a local clustering oracle for signed graphs with such a clear community structure, that can answer membership queries, i.e., \"Given a vertex $v$, which community does $v$ belong to?\", in sublinear time by reading only a small portion of the graph. Formally, when the graph has bounded maximum degree and the number of communities is at most $O(\\log n)$, then with $\\tilde{O}(\\sqrt{n}\\operatorname{poly}(1/\\varepsilon))$ preprocessing time, our oracle can answer each membership query in $\\tilde{O}(\\sqrt{n}\\operatorname{poly}(1/\\varepsilon))$ time, and it correctly classifies a $(1-\\varepsilon)$-fraction of vertices w.r.t. a set of hidden planted ground-truth communities. Our oracle is desirable in applications where the clustering information is needed for only a small number of vertices. Previously, such local clustering oracles were only known for unsigned graphs; our generalization to signed graphs requires a number of new ideas and gives a novel spectral analysis of the behavior of random walks with signs. We evaluate our algorithm for constructing such an oracle and answering membership queries on both synthetic and real-world datasets, validating its performance in practice.","url_abs":"https://arxiv.org/abs/2206.13813v1","url_pdf":"https://arxiv.org/pdf/2206.13813v1.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":"sublinear-time-clustering-oracle-for-signed","repo_url":"https://github.com/stefanresearch/signed-oracle","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2206.13813","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}