{"id":"https://openalex.org/W2963995333","doi":"https://doi.org/10.1109/tsp.2017.2659647","title":"Fast Discrete Distribution Clustering Using Wasserstein Barycenter With Sparse Support","display_name":"Fast Discrete Distribution Clustering Using Wasserstein Barycenter With Sparse Support","publication_year":2017,"publication_date":"2017-01-25","ids":{"openalex":"https://openalex.org/W2963995333","doi":"https://doi.org/10.1109/tsp.2017.2659647","mag":"2963995333"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2017.2659647","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2017.2659647","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031373536","display_name":"Jianbo Ye","orcid":"https://orcid.org/0000-0003-4612-6429"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jianbo Ye","raw_affiliation_strings":["College of Information Sciences and Technology, Pennsylvania State University, University Park, PA, USA"],"affiliations":[{"raw_affiliation_string":"College of Information Sciences and Technology, Pennsylvania State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020822198","display_name":"Panruo Wu","orcid":"https://orcid.org/0000-0003-1859-3580"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Panruo Wu","raw_affiliation_strings":["Department of Computer Science and Engineering, University of California, Riverside, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, University of California, Riverside, CA, USA","institution_ids":["https://openalex.org/I103635307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100687159","display_name":"James Z. Wang","orcid":"https://orcid.org/0000-0003-4379-4173"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Z. Wang","raw_affiliation_strings":["College of Information Sciences and Technology, Pennsylvania State University, University Park, PA, USA"],"affiliations":[{"raw_affiliation_string":"College of Information Sciences and Technology, Pennsylvania State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059344854","display_name":"Jia Li","orcid":"https://orcid.org/0000-0002-4346-8696"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jia Li","raw_affiliation_strings":["Department of Statistics, Pennsylvania State University, University Park, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, Pennsylvania State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5031373536"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":10.393,"has_fulltext":false,"cited_by_count":105,"citation_normalized_percentile":{"value":0.98514901,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"65","issue":"9","first_page":"2317","last_page":"2332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13282","display_name":"Automated Road and Building Extraction","score":0.9768000245094299,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.975600004196167,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.7475322484970093},{"id":"https://openalex.org/keywords/wasserstein-metric","display_name":"Wasserstein metric","score":0.5395147204399109},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.5039681792259216},{"id":"https://openalex.org/keywords/histogram","display_name":"Histogram","score":0.49783778190612793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49209946393966675},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4904482066631317},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48957523703575134},{"id":"https://openalex.org/keywords/centroid","display_name":"Centroid","score":0.48003068566322327},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.46826866269111633},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.45598652958869934},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.437118262052536},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4352457523345947},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4138241112232208},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3557838797569275},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.30508700013160706},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25518012046813965},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.13487902283668518},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.10433623194694519},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.09541034698486328}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7475322484970093},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.5395147204399109},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.5039681792259216},{"id":"https://openalex.org/C53533937","wikidata":"https://www.wikidata.org/wiki/Q185020","display_name":"Histogram","level":3,"score":0.49783778190612793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49209946393966675},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4904482066631317},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48957523703575134},{"id":"https://openalex.org/C146599234","wikidata":"https://www.wikidata.org/wiki/Q511093","display_name":"Centroid","level":2,"score":0.48003068566322327},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.46826866269111633},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.45598652958869934},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.437118262052536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4352457523345947},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4138241112232208},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3557838797569275},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.30508700013160706},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25518012046813965},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.13487902283668518},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.10433623194694519},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.09541034698486328},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2017.2659647","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2017.2659647","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1825835207","display_name":null,"funder_award_id":"ACI-1053575 (XSEDE)","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1997590966","display_name":null,"funder_award_id":"CCF-0936948","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G216048946","display_name":null,"funder_award_id":"ACI-0821527 (CyberStar)","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G346262037","display_name":null,"funder_award_id":"DMS-1521092","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6811401891","display_name":null,"funder_award_id":"ACI-1027854","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W385466589","https://openalex.org/W658020064","https://openalex.org/W1557595030","https://openalex.org/W1585160083","https://openalex.org/W1629559917","https://openalex.org/W1639961155","https://openalex.org/W1660572054","https://openalex.org/W1968333723","https://openalex.org/W1994166982","https://openalex.org/W2004304255","https://openalex.org/W2006228023","https://openalex.org/W2009172320","https://openalex.org/W2016384870","https://openalex.org/W2033403400","https://openalex.org/W2033468335","https://openalex.org/W2036996178","https://openalex.org/W2073459066","https://openalex.org/W2076845236","https://openalex.org/W2078667299","https://openalex.org/W2087544865","https://openalex.org/W2089559088","https://openalex.org/W2094963775","https://openalex.org/W2096765209","https://openalex.org/W2112980792","https://openalex.org/W2114296159","https://openalex.org/W2126885789","https://openalex.org/W2129250947","https://openalex.org/W2133478409","https://openalex.org/W2138615112","https://openalex.org/W2143668817","https://openalex.org/W2150695437","https://openalex.org/W2153579005","https://openalex.org/W2156036190","https://openalex.org/W2158131535","https://openalex.org/W2162833336","https://openalex.org/W2164278908","https://openalex.org/W2165599843","https://openalex.org/W2169678505","https://openalex.org/W2171852577","https://openalex.org/W2241871771","https://openalex.org/W2250539671","https://openalex.org/W2251013587","https://openalex.org/W2254589950","https://openalex.org/W2298250094","https://openalex.org/W2501030598","https://openalex.org/W2534420330","https://openalex.org/W2539033431","https://openalex.org/W2953057288","https://openalex.org/W4206742934","https://openalex.org/W4235169531","https://openalex.org/W4244030505","https://openalex.org/W4292363360","https://openalex.org/W4294170691","https://openalex.org/W6621906925","https://openalex.org/W6633511732","https://openalex.org/W6636708570","https://openalex.org/W6636749761","https://openalex.org/W6668990524","https://openalex.org/W6674201379","https://openalex.org/W6680970901","https://openalex.org/W6682270173","https://openalex.org/W6682691769","https://openalex.org/W6682962330","https://openalex.org/W6684050148","https://openalex.org/W6684489972","https://openalex.org/W6685529966","https://openalex.org/W6724387602","https://openalex.org/W6728760990","https://openalex.org/W6729109823"],"related_works":["https://openalex.org/W2595172197","https://openalex.org/W2084856301","https://openalex.org/W2127970246","https://openalex.org/W2885125400","https://openalex.org/W1989889224","https://openalex.org/W4382618745","https://openalex.org/W1973775000","https://openalex.org/W2748922771","https://openalex.org/W1987128138","https://openalex.org/W1813751874"],"abstract_inverted_index":{"In":[0,75,95],"a":[1,36,48,58,80,118],"variety":[2],"of":[3,9,38,57,68,92,102,127,153,166],"research":[4],"areas,":[5],"the":[6,12,30,43,52,55,72,87,96,99,103,154,163,167,199],"weighted":[7],"bag":[8],"vectors":[10],"and":[11,107,125,130,137,150,170,175],"histogram":[13],"are":[14,105,133,188],"widely":[15,195],"used":[16,196],"descriptors":[17],"for":[18,35,85,141],"complex":[19],"objects.":[20],"Both":[21],"can":[22],"be":[23],"expressed":[24],"as":[25],"discrete":[26,39,89],"distributions.":[27],"D2-clustering":[28,46],"pursues":[29],"minimum":[31],"total":[32],"within-cluster":[33],"variation":[34],"set":[37],"distributions":[40],"subject":[41],"to":[42,71],"Kantorovich-Wasserstein":[44],"metric.":[45],"has":[47],"severe":[49],"scalability":[50],"issue,":[51],"bottleneck":[53],"being":[54],"computation":[56],"centroid":[59],"distribution,":[60],"called":[61],"Wasserstein":[62,90],"barycenter,":[63],"that":[64],"minimizes":[65],"its":[66,131],"sum":[67],"squared":[69],"distances":[70],"cluster":[73],"members.":[74],"this":[76],"paper,":[77],"we":[78,138,146,161],"develop":[79,147],"modified":[81],"Bregman":[82],"ADMM":[83],"approach":[84],"computing":[86],"approximate":[88],"barycenter":[91],"large":[93],"clusters.":[94],"case":[97],"when":[98],"support":[100],"points":[101],"barycenters":[104],"unknown":[106],"have":[108],"low":[109],"cardinality,":[110],"our":[111,128],"method":[112,129],"achieves":[113],"high":[114],"accuracy":[115],"empirically":[116],"at":[117],"much":[119],"reduced":[120],"computational":[121,164],"cost.":[122],"The":[123,178],"strengths":[124],"weaknesses":[126],"alternatives":[132],"examined":[134],"through":[135],"experiments,":[136],"recommend":[139],"scenarios":[140],"their":[142,172],"respective":[143],"usage.":[144],"Moreover,":[145],"both":[148],"serial":[149],"parallelized":[151],"versions":[152],"algorithm.":[155],"By":[156],"experimenting":[157],"with":[158,193],"large-scale":[159],"data,":[160],"demonstrate":[162],"efficiency":[165],"new":[168],"methods":[169,197],"investigate":[171],"convergence":[173],"properties":[174],"numerical":[176],"stability.":[177],"clustering":[179],"results":[180],"obtained":[181],"on":[182],"several":[183],"datasets":[184],"in":[185,191,198],"different":[186],"domains":[187],"highly":[189],"competitive":[190],"comparison":[192],"some":[194],"corresponding":[200],"areas.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":22},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
