{"id":"https://openalex.org/W2962721123","doi":"https://doi.org/10.1109/tfuzz.2017.2659739","title":"On the Convergence of the Sparse Possibilistic C-Means Algorithm","display_name":"On the Convergence of the Sparse Possibilistic C-Means Algorithm","publication_year":2017,"publication_date":"2017-01-26","ids":{"openalex":"https://openalex.org/W2962721123","doi":"https://doi.org/10.1109/tfuzz.2017.2659739","mag":"2962721123"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2017.2659739","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2017.2659739","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/A5014467125","display_name":"Konstantinos Koutroumbas","orcid":"https://orcid.org/0000-0002-8480-1539"},"institutions":[{"id":"https://openalex.org/I4210118731","display_name":"National Observatory of Athens","ror":"https://ror.org/03dtebk39","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210118731"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Konstantinos D. Koutroumbas","raw_affiliation_strings":["Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Athens, Greece","institution_ids":["https://openalex.org/I4210118731"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035272432","display_name":"Spyridoula D. Xenaki","orcid":"https://orcid.org/0000-0002-1610-0511"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]},{"id":"https://openalex.org/I4210118731","display_name":"National Observatory of Athens","ror":"https://ror.org/03dtebk39","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210118731"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Spyridoula D. Xenaki","raw_affiliation_strings":["Department of Informatics and Telecommunications, National & Kapodistrian University of Athens, Athens, Greece","Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Athens, Greece","Department of Informatics and Telecommunications, National & Kapodistrian University of Athens, Athens, Greece; Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Athens, Greece"],"raw_orcid":"https://orcid.org/0000-0002-1610-0511","affiliations":[{"raw_affiliation_string":"Department of Informatics and Telecommunications, National & Kapodistrian University of Athens, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]},{"raw_affiliation_string":"Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Athens, Greece","institution_ids":["https://openalex.org/I4210118731"]},{"raw_affiliation_string":"Department of Informatics and Telecommunications, National & Kapodistrian University of Athens, Athens, Greece; Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Athens, Greece","institution_ids":["https://openalex.org/I4210118731","https://openalex.org/I200777214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081131282","display_name":"Athanasios A. Rontogiannis","orcid":"https://orcid.org/0000-0001-6161-4055"},"institutions":[{"id":"https://openalex.org/I4210118731","display_name":"National Observatory of Athens","ror":"https://ror.org/03dtebk39","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210118731"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Athanasios A. Rontogiannis","raw_affiliation_strings":["Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Athens, Greece","institution_ids":["https://openalex.org/I4210118731"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4699,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.88939517,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"26","issue":"1","first_page":"324","last_page":"337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/convergence","display_name":"Convergence (economics)","score":0.8034093379974365},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.7785450220108032},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.712925374507904},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.566016435623169},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47815975546836853},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40709951519966125},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3470749258995056}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.8034093379974365},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.7785450220108032},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.712925374507904},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.566016435623169},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47815975546836853},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40709951519966125},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3470749258995056},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2017.2659739","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2017.2659739","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1574923065","https://openalex.org/W1895360584","https://openalex.org/W1977556410","https://openalex.org/W1979641069","https://openalex.org/W1994615541","https://openalex.org/W2024463451","https://openalex.org/W2027006788","https://openalex.org/W2035028362","https://openalex.org/W2038614136","https://openalex.org/W2040394922","https://openalex.org/W2043230024","https://openalex.org/W2113076747","https://openalex.org/W2120688485","https://openalex.org/W2125836384","https://openalex.org/W2157015572","https://openalex.org/W2167428023","https://openalex.org/W2170975407","https://openalex.org/W2802627035"],"related_works":["https://openalex.org/W2799781502","https://openalex.org/W2035564297","https://openalex.org/W4226459360","https://openalex.org/W1587627601","https://openalex.org/W1521205480","https://openalex.org/W2020468680","https://openalex.org/W2018228211","https://openalex.org/W2001264248","https://openalex.org/W2108861020","https://openalex.org/W2378960857"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,69],"convergence":[4,46,77],"proof":[5],"for":[6,51,79],"the":[7,25,32,52,76],"recently":[8],"proposed":[9,58],"cost":[10,38],"function":[11],"optimization":[12],"sparse":[13],"possibilistic":[14,54],"c-means":[15,55],"(SPCM)":[16],"algorithm":[17,26,57],"is":[18,22,41],"provided.":[19],"Specifically,":[20],"it":[21,67],"shown":[23,43],"that":[24,44,75],"will":[27],"converge":[28],"to":[29],"one":[30],"of":[31,35,72],"local":[33],"minima":[34],"its":[36],"associated":[37],"function.":[39],"It":[40],"also":[42],"similar":[45],"results":[47,78],"can":[48],"be":[49],"derived":[50],"well-known":[53],"(PCM)":[56],"by":[59],"Krishnapuram":[60],"and":[61],"Keller,":[62],"1996,":[63],"if":[64],"we":[65],"view":[66],"as":[68],"special":[70],"case":[71],"SPCM.":[73],"Note":[74],"PCM":[80],"are":[81],"stronger":[82],"than":[83],"those":[84],"established":[85],"in":[86],"previous":[87],"works.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":8},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}