{"id":"https://openalex.org/W2074638406","doi":"https://doi.org/10.1109/tfuzz.2014.2360723","title":"Quadratic Program-Based Modularity Maximization for Fuzzy Community Detection in Social Networks","display_name":"Quadratic Program-Based Modularity Maximization for Fuzzy Community Detection in Social Networks","publication_year":2014,"publication_date":"2014-09-29","ids":{"openalex":"https://openalex.org/W2074638406","doi":"https://doi.org/10.1109/tfuzz.2014.2360723","mag":"2074638406"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2014.2360723","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2014.2360723","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy Systems","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/A5018866702","display_name":"Jianhai Su","orcid":null},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianhai Su","raw_affiliation_strings":["Department of Computer Science, Michigan Technological University, Houghton, MI, USA","McAfee, Inc., Santa Clara, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Michigan Technological University, Houghton, MI, USA","institution_ids":["https://openalex.org/I11957088"]},{"raw_affiliation_string":"McAfee, Inc., Santa Clara, CA, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060923133","display_name":"Timothy C. Havens","orcid":"https://orcid.org/0000-0002-5746-3749"},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Timothy C. Havens","raw_affiliation_strings":["Departments of Electrical and Computer Engineering and Computer Science, Michigan Technological University, Houghton, MI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Electrical and Computer Engineering and Computer Science, Michigan Technological University, Houghton, MI, USA","institution_ids":["https://openalex.org/I11957088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I11957088"],"apc_list":null,"apc_paid":null,"fwci":1.9351,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.86152107,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"23","issue":"5","first_page":"1356","last_page":"1371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11644","display_name":"Spam and Phishing Detection","score":0.97079998254776,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T10664","display_name":"Sentiment Analysis and Opinion Mining","score":0.9545000195503235,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity (biology)","score":0.6416773796081543},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.6051857471466064},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.585415244102478},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5390585660934448},{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.5067682862281799},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4953095018863678},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49339333176612854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42878690361976624},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40383797883987427},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22780534625053406},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20629894733428955}],"concepts":[{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.6416773796081543},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.6051857471466064},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.585415244102478},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5390585660934448},{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.5067682862281799},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4953095018863678},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49339333176612854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42878690361976624},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40383797883987427},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22780534625053406},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20629894733428955},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tfuzz.2014.2360723","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2014.2360723","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy Systems","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.mtu.edu:michigantech-p-2047","is_oa":false,"landing_page_url":"https://digitalcommons.mtu.edu/michigantech-p/1050","pdf_url":null,"source":{"id":"https://openalex.org/S4377196391","display_name":"Digital Commons - Michigan Tech (Michigan Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11957088","host_organization_name":"Michigan Technological University","host_organization_lineage":["https://openalex.org/I11957088"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Michigan Tech Publications, Part 1","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W5891020","https://openalex.org/W80507587","https://openalex.org/W1491635691","https://openalex.org/W1508853606","https://openalex.org/W1612336946","https://openalex.org/W1967140769","https://openalex.org/W1971421925","https://openalex.org/W1977713568","https://openalex.org/W1978119584","https://openalex.org/W1985625141","https://openalex.org/W1993200481","https://openalex.org/W2000560314","https://openalex.org/W2001017535","https://openalex.org/W2013307517","https://openalex.org/W2015953751","https://openalex.org/W2020323825","https://openalex.org/W2042276255","https://openalex.org/W2044061073","https://openalex.org/W2044719661","https://openalex.org/W2044783742","https://openalex.org/W2045971059","https://openalex.org/W2050095729","https://openalex.org/W2061211758","https://openalex.org/W2075023395","https://openalex.org/W2094234423","https://openalex.org/W2095293504","https://openalex.org/W2105201056","https://openalex.org/W2119669490","https://openalex.org/W2120698362","https://openalex.org/W2127048411","https://openalex.org/W2131681506","https://openalex.org/W2142170653","https://openalex.org/W2143969840","https://openalex.org/W2155167324","https://openalex.org/W2165452678","https://openalex.org/W2170590171","https://openalex.org/W2752853835","https://openalex.org/W3021014091","https://openalex.org/W3098935589","https://openalex.org/W3099768174","https://openalex.org/W3100069540","https://openalex.org/W3101413764","https://openalex.org/W3102641634","https://openalex.org/W3105411815","https://openalex.org/W4292081303","https://openalex.org/W4299352187","https://openalex.org/W6600242124","https://openalex.org/W6636572641"],"related_works":["https://openalex.org/W241127407","https://openalex.org/W2381035939","https://openalex.org/W1521824362","https://openalex.org/W2468477307","https://openalex.org/W2910645127","https://openalex.org/W162895179","https://openalex.org/W3177799343","https://openalex.org/W3119198325","https://openalex.org/W623642078","https://openalex.org/W2133728917"],"abstract_inverted_index":{"One":[0],"of":[1,6,16,53,88,149,171,212,218,232,254,276,285],"the":[2,28,72,104,112,168,210,213,255,277,310,321],"most":[3,183],"important":[4],"elements":[5],"social":[7,113],"network":[8],"analysis":[9],"is":[10,130,157,173,180,260,309],"community":[11,35,220,235,313],"detection,":[12,36],"i.e.,":[13,197],"finding":[14],"groups":[15],"similar":[17],"people":[18],"based":[19,92,242],"on":[20,93,246],"their":[21],"traits.":[22],"In":[23],"this":[24,188],"paper,":[25],"we":[26,190],"present":[27],"fuzzy":[29,43,234,307,312,324],"modularity":[30,99],"maximization":[31,100],"(FMM)":[32],"approach":[33],"for":[34,82,108,165,182],"which":[37,102,129,146,199],"finds":[38,161,306],"overlapping":[39],"-":[40,44],"that":[41,117,159,252,318],"is,":[42],"communities":[45],"(where":[46],"appropriate)":[47],"by":[48],"maximizing":[49],"a":[50,62,67,83,94,123,137,153],"generalized":[51],"form":[52],"Newman's":[54],"modularity.":[55],"The":[56],"first":[57],"proposed":[58,74,95],"FMM":[59],"solution":[60,75],"uses":[61,76],"tree-based":[63,138,154],"structure":[64],"to":[65,79,203,316],"find":[66,320],"globally":[68,162],"optimal":[69,85,105,163],"solution,":[70],"while":[71],"second":[73],"alternating":[77,194],"optimization":[78,127,195],"efficiently":[80],"search":[81],"locally":[84],"solution.":[86],"Both":[87],"these":[89],"approaches":[90],"are":[91,200,280],"algorithm":[96,315],"called":[97,140,238],"one-step":[98],"(OSMM),":[101],"computes":[103],"cluster":[106],"memberships":[107],"one":[109,253],"person":[110],"in":[111,152,290],"network.":[114],"We":[115,134,208,250],"prove":[116],"OSMM":[118,150],"can":[119,319],"be":[120,204],"formulated":[121],"as":[122],"simplified":[124],"quadratic":[125],"knapsack":[126],"problem,":[128],"O(n)":[131],"time":[132,169,206],"complexity.":[133,207],"then":[135],"propose":[136,191],"algorithm,":[139],"FMM/Find":[141],"Best":[142],"Leaf":[143],"Node":[144],"(FMM/FBLN),":[145],"represents":[147],"sequences":[148],"steps":[151],"structure.":[155],"It":[156],"proved":[158],"FMM/FBLN":[160,172],"solutions":[164,215],"FMM;":[166],"however,":[167],"complexity":[170],"O(nd),":[174],"d":[175],"\u2265":[176],"2;":[177],"thus,":[178],"it":[179],"impractical":[181],"real-world":[184,248],"networks.":[185],"To":[186],"combat":[187],"inefficiency,":[189],"five":[192,256],"heuristic-based":[193],"schemes,":[196],"FMM/H1-H5,":[198],"all":[201,275],"shown":[202],"O(n2)":[205],"compare":[209],"results":[211],"FMM/H":[214,278],"with":[216,230,263],"those":[217,231],"state-of-the-art":[219],"detection":[221,236,314],"algorithms,":[222],"MULTICUT":[223],"spectral":[224],"FCM":[225],"(MSFCM)":[226],"and":[227,229,240,265,272,302],"GALS,":[228],"two":[233,283],"algorithms":[237,258],"GA":[239],"vertex-similarity":[241],"gradient-descent":[243],"method":[244],"(VSGD)":[245],"ten":[247],"datasets.":[249],"conclude":[251],"heuristic":[257],"(FMM/H2)":[259],"very":[261],"competitive":[262],"GALS":[264,289,296],"much":[266],"more":[267],"effective":[268],"than":[269,288],"MSFCM,":[270],"GA,":[271],"VSGD.":[273],"Furthermore,":[274],"schemes":[279],"at":[281],"least":[282],"orders":[284],"magnitude":[286],"faster":[287],"run":[291],"time.":[292],"Finally,":[293],"FMM/H,":[294],"unlike":[295],"(which":[297,304],"only":[298,311],"produces":[299],"crisp":[300],"partitions)":[301],"MSFCM":[303],"always":[305],"partitions),":[308],"date":[317],"max-modularity":[322],"partition,":[323],"or":[325],"crisp.":[326]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}