[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8,"_9":10},"actionData","errors","root",{"_284":285},"routes/_layout",{"_11":204},"routes/entity.$type.$id",{"_11":12,"_13":14,"_15":16,"_17":18,"_19":20,"_21":22,"_23":24,"_25":26,"_27":28},"dehydratedState",{"_72":73,"_74":75},"type","paper","id","paper_W2962911132","section","technologies","entity",{"_15":16,"_29":30,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":38,"_39":-5,"_40":41,"_42":43,"_44":45,"_46":47,"_48":-5,"_49":50,"_51":30,"_52":53,"_54":55,"_56":57,"_58":-5,"_59":60,"_61":-5,"_62":63,"_64":-5,"_65":66,"_67":30,"_68":-5},"canonical","https://www.hugmap.com/entity/paper/paper_W2962911132/technologies","siteBaseUrl","https://www.hugmap.com","sectionCount",2,"jsonLd","{\"@context\":\"https://schema.org\",\"@graph\":[{\"name\":\"Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W2962911132/technologies\",\"@type\":\"ScholarlyArticle\",\"headline\":\"Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering\",\"datePublished\":\"2016-06-01\"},{\"@type\":\"CollectionPage\",\"name\":\"Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering 相关技术\",\"description\":\"Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering 在 HugMap 中的相关技术，共 2 条，含结构化关联信息与详情链接。\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W2962911132/technologies\",\"inLanguage\":\"zh-CN\"},{\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"首页\",\"item\":\"https://www.hugmap.com/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"论文\",\"item\":\"https://www.hugmap.com/search?type=paper\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W2962911132\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"相关技术\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W2962911132/technologies\"}]}]}","name","Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering","nameZh","aliases","description","descriptionZh","status","active","externalIds","{\"openalex\":\"W2962911132\",\"doi\":\"10.1109/cvpr.2016.426\"}","properties","source","openalex","createdAt","2026-05-22T13:51:37.221382749","updatedAt","2026-05-22T13:51:37.221384331","doi","10.1109/cvpr.2016.426","arxivId","openalexId","W2962911132","title","abstractText","State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with ℓ ₁ , ℓ ₂ or nuclear norms. ℓ ₁ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be connected. ℓ ₂ and nuclear norm regularization often improve connectivity, but give a subspace-preserving affinity only for independent subspaces. Mixed ℓ ₁ , ℓ ₂ and nuclear norm regularizations offer a balance between the subspace-preserving and connectedness properties, but this comes at the cost of increased computational complexity. This paper studies the geometry of the elastic net regularizer (a mixture of the ℓ ₁ and ℓ ₂ norms) and uses it to derive a provably correct and scalable active set method for finding the optimal coefficients. Our geometric analysis also provides a theoretical justification and a geometric interpretation for the balance between the connectedness (due to ℓ ₂ regularization) and subspace-preserving (due to ℓ ₁ regularization) properties for elastic net subspace clustering. Our experiments show that the proposed active set method not only achieves state-of-the-art clustering performance, but also efficiently handles large-scale datasets.","publishedDate","2016-06-01","publishedYear",2016,"venue","citationCount",246,"authors","keywords",[69,70,71],"pdfUrl","topVenue",false,"displayName","displayDescription","Advanced Computing and Algorithms","Complex Network Analysis Techniques","Topological and Geometric Data Analysis","mutations",[],"queries",[76],{"_77":78,"_79":80,"_81":82,"_83":84},"dehydratedAt",1781735046175,"state",{"_86":87,"_88":89,"_90":78,"_91":-5,"_92":93,"_94":93,"_95":93,"_96":-5,"_97":-5,"_98":66,"_35":99,"_100":101},"queryKey",[85,19,14,16],"queryHash","[\"portal\",\"entity\",\"paper\",\"paper_W2962911132\"]","portal","data",{"_19":20,"_102":103,"_104":105,"_106":107,"_108":109,"_18":110,"_61":111},"dataUpdateCount",1,"dataUpdatedAt","error","errorUpdateCount",0,"errorUpdatedAt","fetchFailureCount","fetchFailureReason","fetchMeta","isInvalidated","success","fetchStatus","idle","entityType","Paper","taxonomies",[171,172,173],"events",[],"articles",[],[149,150],[112,113,114,115],{"_15":143,"_29":144,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":145,"_39":-5,"_40":41,"_42":146,"_44":147,"_121":148,"_51":-5,"_123":-5,"_124":-5,"_125":-5,"_59":-5,"_126":-5,"_127":-5,"_128":-5,"_129":-5,"_130":-5,"_67":144,"_68":-5},{"_15":137,"_29":138,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":139,"_39":-5,"_40":41,"_42":140,"_44":141,"_121":142,"_51":-5,"_123":-5,"_124":-5,"_125":-5,"_59":-5,"_126":-5,"_127":-5,"_128":-5,"_129":-5,"_130":-5,"_67":138,"_68":-5},{"_15":131,"_29":132,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":133,"_39":-5,"_40":41,"_42":134,"_44":135,"_121":136,"_51":-5,"_123":-5,"_124":-5,"_125":-5,"_59":-5,"_126":-5,"_127":-5,"_128":-5,"_129":-5,"_130":-5,"_67":132,"_68":-5},{"_15":116,"_29":117,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":118,"_39":-5,"_40":41,"_42":119,"_44":120,"_121":122,"_51":-5,"_123":-5,"_124":-5,"_125":-5,"_59":-5,"_126":-5,"_127":-5,"_128":-5,"_129":-5,"_130":-5,"_67":117,"_68":-5},"person_A5103110999","Chong You","{\"openalex\":\"A5103110999\",\"orcid\":\"0000-0001-7821-2378\"}","2026-05-19T17:08:57.515000361","2026-05-22T15:46:47.213923301","orcid","0000-0001-7821-2378","affiliation","researchArea","paperCount","homepage","linkedin","twitter","github","hindex","person_A5100654344","Chun-Guang Li","{\"openalex\":\"A5100654344\",\"orcid\":\"0000-0002-5716-268X\"}","2026-05-16T03:32:07.177836917","2026-05-22T15:46:47.210198311","0000-0002-5716-268X","person_A5082367556","Daniel P. Robinson","{\"openalex\":\"A5082367556\",\"orcid\":\"0000-0003-0251-4227\"}","2026-05-19T17:08:58.178030022","2026-05-22T13:51:37.244876364","0000-0003-0251-4227","person_A5011256828","Renè Vidal","{\"openalex\":\"A5011256828\",\"orcid\":\"0000-0003-1838-0761\"}","2026-05-14T02:31:14.374397161","2026-05-23T11:13:13.209038801","0000-0003-1838-0761",{"_15":165,"_29":69,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":166,"_39":-5,"_40":153,"_42":167,"_44":168,"_156":169,"_158":170,"_160":-5,"_161":162,"_163":-5,"_125":-5,"_164":-5,"_67":69,"_68":-5},{"_15":151,"_29":70,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":152,"_39":-5,"_40":153,"_42":154,"_44":155,"_156":157,"_158":159,"_160":-5,"_161":162,"_163":-5,"_125":-5,"_164":-5,"_67":70,"_68":-5},"tech_oa_T10064","{\"taxonomy_id\":\"tax_rd_T10064\"}","openalex_topics","2026-05-17T09:00:21.21739167","2026-05-17T09:00:21.217393598","techType","architecture","domain","Physical Sciences","proposedYear","maturityLevel","growing","wikipediaUrl","patentCount","tech_oa_T13731","{\"taxonomy_id\":\"tax_rd_T13731\"}","2026-05-17T09:00:52.252591733","2026-05-17T09:00:52.252594113","algorithm","Social Sciences",{"_15":198,"_29":70,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":199,"_39":-5,"_40":41,"_42":200,"_44":201,"_178":179,"_180":-5,"_181":182,"_183":202,"_185":203,"_187":93,"_188":189,"_190":93,"_191":-5,"_67":70,"_68":-5},{"_15":192,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":193,"_39":-5,"_40":41,"_42":194,"_44":195,"_178":179,"_180":-5,"_181":182,"_183":196,"_185":197,"_187":93,"_188":189,"_190":93,"_191":-5,"_67":71,"_68":-5},{"_15":174,"_29":69,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":175,"_39":-5,"_40":41,"_42":176,"_44":177,"_178":179,"_180":-5,"_181":182,"_183":184,"_185":186,"_187":93,"_188":189,"_190":93,"_191":-5,"_67":69,"_68":-5},"tax_rd_T13731","{\"openalex_topic\":\"T13731\"}","2026-05-14T06:33:20.341361751","2026-05-23T11:54:17.231193771","taxonomyType","RESEARCH_DOMAIN","code","level",3,"parentId","tax_rd_3322","path","Social Sciences/Social Sciences/Urban Studies/Advanced Computing and Algorithms","sortOrder","isLeaf",true,"entityCount","children","tax_rd_T12536","{\"openalex_topic\":\"T12536\"}","2026-05-14T00:39:20.305168512","2026-05-23T11:54:41.259433511","tax_rd_1703","Physical Sciences/Computer Science/Computational Theory and Mathematics/Topological and Geometric Data Analysis","tax_rd_T10064","{\"openalex_topic\":\"T10064\"}","2026-05-14T00:32:00.37102808","2026-05-23T11:56:06.240435905","tax_rd_3109","Physical Sciences/Physics and Astronomy/Statistical and Nonlinear Physics/Complex Network Analysis Techniques",{"_72":205,"_74":206},[],[207],{"_77":208,"_79":209,"_81":210,"_83":211},1781735043248,{"_86":213,"_88":89,"_90":208,"_91":-5,"_92":93,"_94":93,"_95":93,"_96":-5,"_97":-5,"_98":66,"_35":99,"_100":101},[85,212],"[\"portal\",\"industries\"]","industries",[214,215,216,217,218,219,220,221,222,223,224,225],{"_15":277,"_29":278,"_31":-5,"_32":279,"_33":280,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":281,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":278,"_68":280},{"_15":273,"_29":274,"_31":-5,"_32":-5,"_33":275,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":276,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":274,"_68":275},{"_15":267,"_29":268,"_31":-5,"_32":269,"_33":270,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":271,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":268,"_68":270},{"_15":263,"_29":264,"_31":-5,"_32":-5,"_33":265,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":266,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":264,"_68":265},{"_15":259,"_29":260,"_31":-5,"_32":-5,"_33":261,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":262,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":260,"_68":261},{"_15":253,"_29":254,"_31":-5,"_32":255,"_33":256,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":257,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":254,"_68":256},{"_15":249,"_29":250,"_31":-5,"_32":-5,"_33":251,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":252,"_187":93,"_188":189,"_190":93,"_191":-5,"_67":250,"_68":251},{"_15":245,"_29":246,"_31":-5,"_32":-5,"_33":247,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":248,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":246,"_68":247},{"_15":241,"_29":242,"_31":-5,"_32":-5,"_33":243,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":244,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":242,"_68":243},{"_15":237,"_29":238,"_31":-5,"_32":-5,"_33":239,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":240,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":238,"_68":239},{"_15":233,"_29":234,"_31":-5,"_32":-5,"_33":235,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":236,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":234,"_68":235},{"_15":226,"_29":227,"_31":-5,"_32":-5,"_33":228,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":229,"_42":-5,"_44":-5,"_178":230,"_180":-5,"_181":89,"_183":231,"_185":232,"_187":93,"_188":66,"_190":93,"_191":-5,"_67":227,"_68":228},"tax_ind_smartphone","智能手机","Smartphone","manual","INDUSTRY","tax_ind_root","科技行业/智能手机","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_quantum","量子计算","Quantum Computing","科技行业/量子计算","tax_ind_blockchain","区块链",[258],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_security","网络安全","Cybersecurity","科技行业/网络安全","tax_ind_semi","半导体",[272],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[282,283],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_286":24},"SITE_BASE_URL"]

Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering 论文

Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering · 相关技术

相关技术