{"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/graph-sketching-based-space-efficient-data","title":"Graph sketching-based Space-efficient Data Clustering","arxiv_id":"1703.02375","date":"2017-03-07","proceeding":null,"authors":["Anne Morvan","Krzysztof Choromanski","Cédric Gouy-Pailler","Jamal Atif"],"abstract":"In this paper, we address the problem of recovering arbitrary-shaped data\nclusters from datasets while facing \\emph{high space constraints}, as this is\nfor instance the case in many real-world applications when analysis algorithms\nare directly deployed on resources-limited mobile devices collecting the data.\nWe present DBMSTClu a new space-efficient density-based \\emph{non-parametric}\nmethod working on a Minimum Spanning Tree (MST) recovered from a limited number\nof linear measurements i.e. a \\emph{sketched} version of the dissimilarity\ngraph $\\mathcal{G}$ between the $N$ objects to cluster. Unlike $k$-means,\n$k$-medians or $k$-medoids algorithms, it does not fail at distinguishing\nclusters with particular forms thanks to the property of the MST for expressing\nthe underlying structure of a graph. No input parameter is needed contrarily to\nDBSCAN or the Spectral Clustering method. An approximate MST is retrieved by\nfollowing the dynamic \\emph{semi-streaming} model in handling the dissimilarity\ngraph $\\mathcal{G}$ as a stream of edge weight updates which is sketched in one\npass over the data into a compact structure requiring $O(N\n\\operatorname{polylog}(N))$ space, far better than the theoretical memory cost\n$O(N^2)$ of $\\mathcal{G}$. The recovered approximate MST $\\mathcal{T}$ as\ninput, DBMSTClu then successfully detects the right number of nonconvex\nclusters by performing relevant cuts on $\\mathcal{T}$ in a time linear in $N$.\nWe provide theoretical guarantees on the quality of the clustering partition\nand also demonstrate its advantage over the existing state-of-the-art on\nseveral datasets.","url_abs":"http://arxiv.org/abs/1703.02375v5","url_pdf":"http://arxiv.org/pdf/1703.02375v5.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":"graph-sketching-based-space-efficient-data","repo_url":"https://github.com/annemorvan/DBMSTClu","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[{"method_slug":"spectral-clustering","method_name":"Spectral Clustering"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}