{"id":"https://openalex.org/W1992545447","doi":"https://doi.org/10.1109/ssp.2012.6319638","title":"Of the largest eigenvalue for modularity-based partitioning","display_name":"Of the largest eigenvalue for modularity-based partitioning","publication_year":2012,"publication_date":"2012-08-01","ids":{"openalex":"https://openalex.org/W1992545447","doi":"https://doi.org/10.1109/ssp.2012.6319638","mag":"1992545447"},"language":"en","primary_location":{"id":"doi:10.1109/ssp.2012.6319638","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ssp.2012.6319638","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Statistical Signal Processing Workshop (SSP)","raw_type":"proceedings-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/A5101758877","display_name":"Yu-Teng Chang","orcid":"https://orcid.org/0000-0002-3216-6916"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yu-Teng Chang","raw_affiliation_strings":["Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, USA","Signal and Image Processing Institute, University of Southern California, Los Angeles, .USA"],"affiliations":[{"raw_affiliation_string":"Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Signal and Image Processing Institute, University of Southern California, Los Angeles, .USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030177736","display_name":"Dimitrios Pantazis","orcid":"https://orcid.org/0000-0001-8246-8878"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"id":"https://openalex.org/I144112489","display_name":"McGovern Institute for Brain Research","ror":"https://ror.org/05ymca674","country_code":"US","type":"facility","lineage":["https://openalex.org/I144112489","https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dimitrios Pantazis","raw_affiliation_strings":["McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, USA","[McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, USA]"],"affiliations":[{"raw_affiliation_string":"McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I144112489","https://openalex.org/I63966007"]},{"raw_affiliation_string":"[McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, USA]","institution_ids":["https://openalex.org/I144112489"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054387045","display_name":"Richard M. Leahy","orcid":"https://orcid.org/0000-0002-7278-5471"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard M. Leahy","raw_affiliation_strings":["Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, USA","Signal and Image Processing Institute, University of Southern California, Los Angeles, .USA"],"affiliations":[{"raw_affiliation_string":"Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Signal and Image Processing Institute, University of Southern California, Los Angeles, .USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101758877"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":0.2425,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.53063009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"18","issue":null,"first_page":"125","last_page":"128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.996999979019165,"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":0.996999979019165,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9821000099182129,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9821000099182129,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/adjacency-matrix","display_name":"Adjacency matrix","score":0.8066245317459106},{"id":"https://openalex.org/keywords/spectral-clustering","display_name":"Spectral clustering","score":0.7696895599365234},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7040774822235107},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.6363521814346313},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6132693290710449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5781263113021851},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.560476541519165},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.50057053565979},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.4744252562522888},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.4693542420864105},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4401223659515381},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38270384073257446},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33066052198410034},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2796304225921631},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13767609000205994},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09950557351112366}],"concepts":[{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.8066245317459106},{"id":"https://openalex.org/C105611402","wikidata":"https://www.wikidata.org/wiki/Q2976589","display_name":"Spectral clustering","level":3,"score":0.7696895599365234},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7040774822235107},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.6363521814346313},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6132693290710449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5781263113021851},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.560476541519165},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.50057053565979},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.4744252562522888},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.4693542420864105},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4401223659515381},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38270384073257446},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33066052198410034},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2796304225921631},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13767609000205994},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09950557351112366},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ssp.2012.6319638","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ssp.2012.6319638","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Statistical Signal Processing Workshop (SSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W166475061","https://openalex.org/W608270061","https://openalex.org/W1999320979","https://openalex.org/W2074032719","https://openalex.org/W2111642621","https://openalex.org/W2121947440","https://openalex.org/W2125531986","https://openalex.org/W2132914434","https://openalex.org/W2136088806","https://openalex.org/W2151936673","https://openalex.org/W2962960989","https://openalex.org/W3101413764"],"related_works":["https://openalex.org/W4213150077","https://openalex.org/W2369410163","https://openalex.org/W2059018062","https://openalex.org/W2078477160","https://openalex.org/W2963002212","https://openalex.org/W1989103179","https://openalex.org/W3168808485","https://openalex.org/W3017750840","https://openalex.org/W2604585036","https://openalex.org/W4352976663"],"abstract_inverted_index":{"Despite":[0],"the":[1,15,24,30,34,47,50,77,81,93,96,114],"popularity":[2],"and":[3],"broad":[4],"range":[5],"of":[6,18,26,49,68,80,84,95,99],"spectral":[7,104],"clustering":[8,19,22],"algorithms,":[9],"there":[10],"is":[11,56],"little":[12],"work":[13],"addressing":[14],"statistical":[16],"significance":[17],"results.":[20],"Spectral":[21],"uses":[23],"eigenvalues":[25],"matrices,":[27],"such":[28],"as":[29],"Laplacian":[31],"graph":[32],"or":[33],"adjacency":[35],"matrix":[36,60],"minus":[37],"a":[38,43,66],"null":[39],"model,":[40],"to":[41,91],"partition":[42],"network.":[44],"Even":[45],"though":[46],"distribution":[48,94],"largest":[51,82,97],"eigenvalue":[52,83,98],"for":[53,65,102],"these":[54],"matrices":[55,69,100],"not":[57],"known,":[58],"random":[59,72,86],"theory":[61],"provides":[62],"analytical":[63],"formulas":[64,111],"family":[67],"called":[70],"Gaussian":[71,85],"ensembles.":[73],"We":[74],"demonstrate":[75],"that":[76,112],"Tracy-Widom":[78],"mapping":[79],"ensembles":[87],"can":[88],"be":[89],"modified":[90],"predict":[92],"used":[101],"modularity-based":[103,120],"clustering.":[105],"Using":[106],"this":[107],"finding":[108],"we":[109],"derive":[110],"control":[113],"type":[115],"I":[116],"error":[117],"rate":[118],"on":[119],"partitions.":[121]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}