[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81537-en":3,"doc-seo-81537-105":30,"detail-sidebar-cat-0-en-105":91},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81537,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782698725881665579",8,"Research & Report","Scalable Varied-Density Clustering via Graph Propagation","Proposes a scalable perspective on varied-density clustering for high-dimensional data by modeling clustering as density-adaptive label propagation over neighborhood graphs. Formally links density-based clustering to graph connectivity, allowing efficient propagation techniques from network science. Introduces a density-aware neighborhood propagation algorithm and uses random projection methods to build approximate neighborhood graphs. Reduces computational cost while preserving clustering quality, scaling to datasets with millions of points in minutes and matching competitive accuracy versus existing baselines.","Scalable Varied-Density Clustering via Graph Propagation  \nNinh Pham  \nUniversity of Auckland Auckland, New Zealand [ninh.pham@auckland.ac.nz](ninh.pham@auckland.ac.nz)  \nYingtao Zheng  \nUniversity of Auckland Auckland, New Zealand [yzhe906@aucklanduni.ac.nz](yzhe906@aucklanduni.ac.nz)  \nHugo Phibbs  \nUniversity of Auckland Auckland, New Zealand [hphi344@aucklanduni.ac.nz](hphi344@aucklanduni.ac.nz)  \narXiv :2508 .02989v1 [ cs .LG] 5 Aug 2025  \nAbstract  \nWe propose a novel perspective on varied-density clustering for high-dimensional data by framing it as a label propagation process in neighborhood graphs that adapt to local density variations. Our method formally connects density-based clustering with graph connectivity, enabling the use of efficient graph propagation techniques developed in network science. To ensure scalability, we introduce a density-aware neighborhood propagation algorithm and leverage advanced random projection methods to construct approximate neighborhood graphs. Our approach significantly reduces computational cost while preserving clustering quality. Empirically, it scales to datasets with millions of points in minutes and achieves competitive accuracy compared to existing baselines.  \n1 Introduction  \nDensity-based clustering [7] identifies clusters as dense regions separated by sparse areas, allowing it to detect arbitrarily shaped clusters and handle noise effectively. Unlike methods like k-means [27], it does not assume spherical clusters or require the number of clusters in advance, making it ideal for complex, real-world data.  \nRepresentative density-based clustering methods, such as DBSCAN [18] and Density Peak Clustering (DPC) [35], can be interpreted as label propagation mechanisms over a graph defined by local density relationships. In this view, clusters are seeded at highdensity points–called core points in DBSCAN or density peaks in DPC–which act as the initial label sources. The labels are then propagated from high-to-low density regions, following the structure of a neighborhood graph, which typically assigns remaining points to the label of its near neighbor with similar densities. This formulation naturally respects the underlying density landscape: labels do not cross low-density regions, allowing the algorithm to discover non-convex clusters and separate noisy or sparse areas. Thus, clustering emerges from how labels flow along high-density paths in the neighborhood graph.  \nConsidering each data point as a node in a graph, DBSCAN or DPC has two primary steps, including (1) constructing an 􀁮 -neighborhood or k-nearest neighbor (kNN) graph to discover density and neighborhood of each node, and (2) propagating cluster labels from dense nodes to sparse nodes. The first step is the main computational bottleneck as forming these neighborhood graphs requires a worst-case 􀀤 (􀀽2 ) time for a dataset of 􀀽 points in high dimensions [29, 43]. This limits the applications of density-based clustering on modern million-point datasets. Prior work has tackled this issue by leveraging randomized techniques, such as random projections [36, 44], hashing [17, 31] or sampling [23, 25, 41], to approximate the graph construction. Other work [2, 12, 19, 22, 28] follow the prune-and-bound strategies based on geometric properties on metric spaces to reduce the number of 􀁮-neighborhood queries while forming clusters.  \nWhile density-based clustering and its approximate variants are effective for discovering arbitrarily shaped clusters, they struggle on datasets with highly varied densities due to their reliance on global parameters. DBSCAN requires a fixed neighborhood radius (􀁮) and minimum points (􀀼􀀸􀀽􀀥􀁃􀁂), which makes it difficult to capture clusters of different densities simultaneously: a setting that works for dense regions may cause sparse clusters to be missed or merged with noise. Similarly, DPC relies on a cutoff distance (􀀳 􀀲) to compute local density and to derive a decision graph to identify clu","cbCaiu2MhoZQAmUZ","https://ap.wps.com/l/cbCaiu2MhoZQAmUZ","pdf",823999,3,1,12,"English","en",105,"# Abstract\n# Introduction\n## Density-based clustering as label propagation\n## Computational bottleneck in neighborhood graph construction\n## Limitations on highly varied densities\n## Related work on heterogeneous-density handling\n## Contribution: PING method","[{\"question\":\"What core idea connects density-based clustering to graph label propagation in this work?\",\"answer\":\"Clusters are seeded at high-density points (e.g., DBSCAN core points or DPC density peaks), and labels propagate from high to low density along a neighborhood graph structure so labels follow dense paths and avoid low-density regions.\"},{\"question\":\"Why does building neighborhood graphs become a major bottleneck for density-based clustering?\",\"answer\":\"Constructing exact neighborhood structures (such as kNN or ε-neighborhood graphs) can require worst-case superlinear time in high dimensions, making it impractical for datasets with millions of points.\"},{\"question\":\"How does PING achieve scalability on varied-density, high-dimensional data?\",\"answer\":\"PING avoids explicit graph materialization using a density-aware label propagation algorithm, and it constructs high-quality approximate neighborhoods using scalable random projection methods combined with efficient ANNS techniques.\"}]",1784174125,30,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"scalable-varied-density-clustering-via-graph-propagation","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"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":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/scalable-varied-density-clustering-via-graph-propagation/81537/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What core idea connects density-based clustering to graph label propagation in this work?","Question",{"text":75,"@type":76},"Clusters are seeded at high-density points (e.g., DBSCAN core points or DPC density peaks), and labels propagate from high to low density along a neighborhood graph structure so labels follow dense paths and avoid low-density regions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why does building neighborhood graphs become a major bottleneck for density-based clustering?",{"text":80,"@type":76},"Constructing exact neighborhood structures (such as kNN or ε-neighborhood graphs) can require worst-case superlinear time in high dimensions, making it impractical for datasets with millions of points.",{"name":82,"@type":73,"acceptedAnswer":83},"How does PING achieve scalability on varied-density, high-dimensional data?",{"text":84,"@type":76},"PING avoids explicit graph materialization using a density-aware label propagation algorithm, and it constructs 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