{"id":"https://openalex.org/W2980992822","doi":"https://doi.org/10.3390/a12100216","title":"Adaptive Clustering via Symmetric Nonnegative Matrix Factorization of the Similarity Matrix","display_name":"Adaptive Clustering via Symmetric Nonnegative Matrix Factorization of the Similarity Matrix","publication_year":2019,"publication_date":"2019-10-17","ids":{"openalex":"https://openalex.org/W2980992822","doi":"https://doi.org/10.3390/a12100216","mag":"2980992822"},"language":"en","primary_location":{"id":"doi:10.3390/a12100216","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a12100216","pdf_url":null,"source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/a12100216","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062916710","display_name":"Paola Favati","orcid":"https://orcid.org/0000-0003-0382-3195"},"institutions":[{"id":"https://openalex.org/I4210130157","display_name":"Institute of Informatics and Telematics","ror":"https://ror.org/02gdcn153","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210130157","https://openalex.org/I4210155236"]},{"id":"https://openalex.org/I4210155236","display_name":"National Research Council","ror":"https://ror.org/04zaypm56","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Paola Favati","raw_affiliation_strings":["Istituto di Informatica e Telematica-Consiglio Nazionale delle Ricerche (IIT-CNR), Via G. Moruzzi 1, 56124 Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0382-3195","affiliations":[{"raw_affiliation_string":"Istituto di Informatica e Telematica-Consiglio Nazionale delle Ricerche (IIT-CNR), Via G. Moruzzi 1, 56124 Pisa, Italy","institution_ids":["https://openalex.org/I4210130157","https://openalex.org/I4210155236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027300466","display_name":"G. Lotti","orcid":"https://orcid.org/0000-0002-3299-1967"},"institutions":[{"id":"https://openalex.org/I124601658","display_name":"University of Parma","ror":"https://ror.org/02k7wn190","country_code":"IT","type":"education","lineage":["https://openalex.org/I124601658"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Grazia Lotti","raw_affiliation_strings":["Dipartimento di Matematica, University of Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy"],"raw_orcid":"https://orcid.org/0000-0002-3299-1967","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, University of Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy","institution_ids":["https://openalex.org/I124601658"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008473020","display_name":"O. Menchi","orcid":null},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Ornella Menchi","raw_affiliation_strings":["Dipartimento di Informatica, University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022387101","display_name":"Francesco Romani","orcid":"https://orcid.org/0000-0001-8890-4490"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Romani","raw_affiliation_strings":["Dipartimento di Informatica, University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0001-8890-4490","affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5062916710"],"corresponding_institution_ids":["https://openalex.org/I4210130157","https://openalex.org/I4210155236"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.452,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.65370553,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"12","issue":"10","first_page":"216","last_page":"216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10057","display_name":"Face and Expression Recognition","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9858999848365784,"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/T10689","display_name":"Remote-Sensing Image Classification","score":0.9800999760627747,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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":0.7410953044891357},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.6587237119674683},{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.6383281350135803},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6182376742362976},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6115868091583252},{"id":"https://openalex.org/keywords/nonnegative-matrix","display_name":"Nonnegative matrix","score":0.5691841840744019},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5367383360862732},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5331522822380066},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5191768407821655},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.483207106590271},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4826093912124634},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4197675883769989},{"id":"https://openalex.org/keywords/biclustering","display_name":"Biclustering","score":0.4135856330394745},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.38373398780822754},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3693488538265228},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36723771691322327},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.36019229888916016},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2791644036769867},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2634361982345581},{"id":"https://openalex.org/keywords/correlation-clustering","display_name":"Correlation clustering","score":0.2488139569759369},{"id":"https://openalex.org/keywords/cure-data-clustering-algorithm","display_name":"CURE data clustering algorithm","score":0.1685996949672699}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7410953044891357},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.6587237119674683},{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.6383281350135803},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6182376742362976},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6115868091583252},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.5691841840744019},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5367383360862732},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5331522822380066},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5191768407821655},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.483207106590271},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4826093912124634},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4197675883769989},{"id":"https://openalex.org/C144817290","wikidata":"https://www.wikidata.org/wiki/Q2976575","display_name":"Biclustering","level":5,"score":0.4135856330394745},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.38373398780822754},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3693488538265228},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36723771691322327},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.36019229888916016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2791644036769867},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2634361982345581},{"id":"https://openalex.org/C94641424","wikidata":"https://www.wikidata.org/wiki/Q5172845","display_name":"Correlation clustering","level":3,"score":0.2488139569759369},{"id":"https://openalex.org/C33704608","wikidata":"https://www.wikidata.org/wiki/Q5014717","display_name":"CURE data clustering algorithm","level":4,"score":0.1685996949672699},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/a12100216","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a12100216","pdf_url":null,"source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:arpi.unipi.it:11568/1013650","is_oa":false,"landing_page_url":"http://hdl.handle.net/11568/1013650","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:541b716c4e8b411abe07385c4082b430","is_oa":true,"landing_page_url":"https://doaj.org/article/541b716c4e8b411abe07385c4082b430","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 12, Iss 10, p 216 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/12/10/216/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/a12100216","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a12100216","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a12100216","pdf_url":null,"source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1504886279","https://openalex.org/W1792862432","https://openalex.org/W1988497044","https://openalex.org/W2010315317","https://openalex.org/W2022712430","https://openalex.org/W2026034143","https://openalex.org/W2051224630","https://openalex.org/W2059745395","https://openalex.org/W2067931421","https://openalex.org/W2076566842","https://openalex.org/W2082639035","https://openalex.org/W2093492509","https://openalex.org/W2113586398","https://openalex.org/W2120816706","https://openalex.org/W2124172487","https://openalex.org/W2135029798","https://openalex.org/W2144351558","https://openalex.org/W2404400936","https://openalex.org/W2804454015","https://openalex.org/W2945278217","https://openalex.org/W2965718088","https://openalex.org/W2980992822","https://openalex.org/W3102357545","https://openalex.org/W4302564868","https://openalex.org/W6638090036"],"related_works":["https://openalex.org/W2127243424","https://openalex.org/W4390394189","https://openalex.org/W3099441337","https://openalex.org/W2731733684","https://openalex.org/W2108919995","https://openalex.org/W2022978200","https://openalex.org/W2083358384","https://openalex.org/W1989034480","https://openalex.org/W4386808492","https://openalex.org/W3000071285"],"abstract_inverted_index":{"The":[0,23,42],"problem":[1],"of":[2,8,12,38,50,55,64],"clustering,":[3],"that":[4],"is,":[5],"the":[6,32,48,62,75,84],"partitioning":[7],"data":[9],"into":[10],"groups":[11],"similar":[13],"objects,":[14],"is":[15,29,44,59,79],"a":[16,39,51,65,67],"key":[17],"step":[18],"for":[19,27,47],"many":[20],"data-mining":[21],"problems.":[22],"algorithm":[24,43],"we":[25],"propose":[26],"clustering":[28],"based":[30],"on":[31],"symmetric":[33],"nonnegative":[34],"matrix":[35],"factorization":[36],"(SymNMF)":[37],"similarity":[40],"matrix.":[41],"first":[45],"presented":[46],"case":[49,63],"prescribed":[52],"number":[53],"k":[54],"clusters,":[56],"then":[57],"it":[58],"extended":[60],"to":[61],"not":[66],"priori":[68],"given":[69],"k.":[70],"A":[71],"heuristic":[72],"approach":[73],"improving":[74],"standard":[76],"multistart":[77],"strategy":[78],"proposed":[80],"and":[81],"validated":[82],"by":[83],"experimentation.":[85]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":4}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
