[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117637-en":3,"doc-seo-117637-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117637,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","Fast Approximate Spectral Clustering for Dynamic Networks","Spectral clustering is widely studied but computationally prohibitive for dynamic graphs. The work shows how to speed up clustering by reusing information from previous cluster assignments, avoiding repeated eigenvector computation. It leverages fast Chebyshev graph filtering of random signals as graph features instead of direct eigendecomposition. The proposed dynamic compressive spectral clustering produces assignments whose quality approximates standard spectral clustering under bounded graph dynamics.","View metadata, citation and similar [papers at ](papers at core.ac.uk)[core.ac.uk](papers at core.ac.uk) brought to you by CORE  \nprovided by Infoscience- École polytechnique fédérale de Lausanne  \nFast Approximate Spectral Clustering for Dynamic Networks  \nLionel Martin 1 Andreas Loukas 1 Pierre Vandergheynst 1  \narXiv : 1706 .0359 1v 1 [ stat .ML] 12 Jun 2017  \nAbstract  \nSpectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by using fast Chebyshev graph 􀀂ltering of random signals. We show that the proposed algorithm achieves clustering assignments with quality approximating that of spectral clustering and that it can yield signi􀀂cant complexity bene􀀂ts when the graph dynamics are appropriately bounded.  \n1. Introduction  \nSpectral clustering (SC) is one of the most well-known methods for clustering multivariate data, with numerous applications in biology (e.g., protein-protein interactions, gene co-expression) and social sciences (e.g., call graphs, political study) among others (Von Luxburg, 2007; Fortunato, 2010) . However, because of its inherent dependence on the spectrum of some large graph, SC is also notoriously slow. This has motivated a surge of research focusing in reducing its complexity, for example using matrix sketching methods (Fowlkes et al., 2004; Li et al., 2011; Gittens et al., 2013) and more recently compressive sensing techniques (Ramasamy & Madhow, 2015; Tremblay et al., 2016) .  \nYet, the clustering complexity is still problematic for dynamic graphs, where the edge set is a function of time. Temporal dynamics constitute an important aspect of many network datasets and should be taken into account in the algorithmic design and analysis. Unfortunately, SC is poorly suited to this setting as eigendecomposition –its main computational bottleneck– has tobe recomputed from scratch whenever the graph is updated, or at least periodically (Ning et al., 2007) . This is a missed opportunity since  \n1´Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland. Correspondence to: Lionel Martin \u003Cli  \nonel.martin@ep􀀃.ch> .  \nTechnical report. Preliminary work only.  \nthe clustering assignments of many real networks change slowly with time, suggesting that successive algorithmic runs wastefully repeat similar computations.  \nMotivated by this observation, this paper proposes an algorithm that reuses information of past cluster assignments to expedite computation. Different from previous work on dynamic clustering, our objective is not to improve the clustering quality, for example by enforcing a temporalsmoothness hypothesis (Chakrabarti et al., 2006; Chi et al., 2007) or by using tensor decompositions (Gauvin et al., 2014; Tu et al., 2016) . On the contrary, we focus entirely on decreasing the computational overhead and aim to produce assignments that are provably close to those of SC.  \nOur work is inspired by the recent idea of sidestepping eigendecomposition by utilizing as features random signals that have been 􀀂ltered over the graph (Tremblay et al., 2016) . Our main argument is that, instead of computing the clustering assignment of a graph G 1 using d 􀀂ltered signals as features, one may utilize a percentage of features of a different graph G2 without signi􀀂cant loss in accuracy, as long as G 1 and G2 are appropriately close. This leads to a natural clustering scheme for time-varying topologies: each new instance of the dynamic graph is clustered using pd signals computed previously and only (1 − p)d new 􀀂ltered signals, where p is a percentage. Moreover, inspired by similar ideas we can also attain further complexity reductions with respect to the graph 􀀂lter design, i.e., by identifying the k-th e","cbCaib7MJPh0S4Is","https://ap.wps.com/l/cbCaib7MJPh0S4Is","pdf",1593785,1,10,"English","en",105,"# Introduction\n# Background\n## Spectral clustering (SC)\n## Fast (compressive) methods","[{\"question\":\"Why is spectral clustering slow for dynamic graphs?\",\"answer\":\"Spectral clustering depends on eigenvectors of a graph Laplacian, which must be recomputed whenever the graph updates, making it costly for time-varying edge sets.\"},{\"question\":\"How does the proposed method reduce computation?\",\"answer\":\"It sidesteps eigendecomposition by using fast Chebyshev filtering of random signals and reuses a portion of features computed for previous graphs to avoid repeating similar computations.\"},{\"question\":\"How is clustering quality related to standard spectral clustering?\",\"answer\":\"The paper provides probabilistic guarantees that the clustering assignments from its compressive/dynamic variants approximate those of spectral clustering, with differences controlled by parameters such as the reused-feature fraction and a spectral similarity metric.\"}]","Fast Approximate Spectral Clustering for Dynamic Networks | PDF",1785677532,25,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"fast-approximate-spectral-clustering-for-dynamic-networks","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/fast-approximate-spectral-clustering-for-dynamic-networks/117637/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-02",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"Why is spectral clustering slow for dynamic graphs?","Question",{"text":76,"@type":77},"Spectral clustering depends on eigenvectors of a graph Laplacian, which must be recomputed whenever the graph updates, making it costly for time-varying edge sets.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the proposed method reduce computation?",{"text":81,"@type":77},"It sidesteps eigendecomposition by using fast Chebyshev filtering of random signals and reuses a portion of features computed for previous graphs to avoid repeating similar computations.",{"name":83,"@type":74,"acceptedAnswer":84},"How is clustering quality related to standard spectral clustering?",{"text":85,"@type":77},"The paper provides probabilistic guarantees that the clustering assignments from its compressive/dynamic variants approximate those of spectral clustering, with differences controlled by parameters such as the reused-feature fraction and a spectral similarity metric.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":21,"slug":134},"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":107,"slug":138},19,"General","general"]