{"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/scalable-laplacian-k-modes","title":"Scalable Laplacian K-modes","arxiv_id":"1810.13044","date":"2018-10-31","proceeding":"NeurIPS 2018 12","authors":["Imtiaz Masud Ziko","Eric Granger","Ismail Ben Ayed"],"abstract":"We advocate Laplacian K-modes for joint clustering and density mode finding,\nand propose a concave-convex relaxation of the problem, which yields a parallel\nalgorithm that scales up to large datasets and high dimensions. We optimize a\ntight bound (auxiliary function) of our relaxation, which, at each iteration,\namounts to computing an independent update for each cluster-assignment\nvariable, with guaranteed convergence. Therefore, our bound optimizer can be\ntrivially distributed for large-scale data sets. Furthermore, we show that the\ndensity modes can be obtained as byproducts of the assignment variables via\nsimple maximum-value operations whose additional computational cost is linear\nin the number of data points. Our formulation does not need storing a full\naffinity matrix and computing its eigenvalue decomposition, neither does it\nperform expensive projection steps and Lagrangian-dual inner iterates for the\nsimplex constraints of each point. Furthermore, unlike mean-shift, our\ndensity-mode estimation does not require inner-loop gradient-ascent iterates.\nIt has a complexity independent of feature-space dimension, yields modes that\nare valid data points in the input set and is applicable to discrete domains as\nwell as arbitrary kernels. We report comprehensive experiments over various\ndata sets, which show that our algorithm yields very competitive performances\nin term of optimization quality (i.e., the value of the discrete-variable\nobjective at convergence) and clustering accuracy.","url_abs":"http://arxiv.org/abs/1810.13044v2","url_pdf":"http://arxiv.org/pdf/1810.13044v2.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":"scalable-laplacian-k-modes","repo_url":"https://github.com/imtiazziko/SLK","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":null,"task_name":"valid"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1810.13044","atlas_url":"https://app.syntology.ai/?focus=1810.13044","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1810.13044"}},"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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/imtiazziko/SLK","reach":null}],"summary":{"ran_violates":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"592db688de001c36","entry":"normalizefea","repo":"imtiazziko/SLK","repo_kind":"official","path":"src/SLK.py","file_url":"https://github.com/imtiazziko/SLK/blob/HEAD/src/SLK.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"592db688de001c36"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}