{"id":"https://openalex.org/W1985997397","doi":"https://doi.org/10.1007/s11075-013-9704-0","title":"Nonnegative rank factorization\u2014a heuristic approach via rank reduction","display_name":"Nonnegative rank factorization\u2014a heuristic approach via rank reduction","publication_year":2013,"publication_date":"2013-03-26","ids":{"openalex":"https://openalex.org/W1985997397","doi":"https://doi.org/10.1007/s11075-013-9704-0","mag":"1985997397"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-013-9704-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-013-9704-0","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5101734718","display_name":"Bo Dong","orcid":"https://orcid.org/0000-0003-1679-2818"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bo Dong","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian, China","School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning, 116024, China","School of Mathematical Sciences , Dalian University of Technology , Dalian , China , 116024"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning, 116024, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Mathematical Sciences , Dalian University of Technology , Dalian , China , 116024","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080854365","display_name":"Matthew M. Lin","orcid":"https://orcid.org/0000-0002-8144-947X"},"institutions":[{"id":"https://openalex.org/I148099254","display_name":"National Chung Cheng University","ror":"https://ror.org/0028v3876","country_code":"TW","type":"education","lineage":["https://openalex.org/I148099254"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Matthew M. Lin","raw_affiliation_strings":["Department of Mathematics, National Chung Cheng University, Chia-Yi, 621, Taiwan","Department of Mathematics, National Chung Cheng University, Chia-Yi, Taiwan","Department of Mathematics, National Chung Cheng University, Chia-Yi, Taiwan 621#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Chung Cheng University, Chia-Yi, 621, Taiwan","institution_ids":["https://openalex.org/I148099254"]},{"raw_affiliation_string":"Department of Mathematics, National Chung Cheng University, Chia-Yi, Taiwan","institution_ids":["https://openalex.org/I148099254"]},{"raw_affiliation_string":"Department of Mathematics, National Chung Cheng University, Chia-Yi, Taiwan 621#TAB#","institution_ids":["https://openalex.org/I148099254"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029654954","display_name":"Moody T. Chu","orcid":"https://orcid.org/0000-0001-8544-3588"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Moody T. Chu","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA","Department of Mathematics, North Carolina State University, Raleigh, USA","Department of Mathematics, North Carolina State University, Raleigh, USA 27695-8205"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, USA","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, USA 27695-8205","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029654954","https://openalex.org/A5080854365","https://openalex.org/A5101734718"],"corresponding_institution_ids":["https://openalex.org/I137902535","https://openalex.org/I148099254","https://openalex.org/I27357992"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.3725,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.62793349,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"65","issue":"2","first_page":"251","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9962999820709229,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9962999820709229,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9927999973297119,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8252376317977905},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.8000091314315796},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6337782144546509},{"id":"https://openalex.org/keywords/nonnegative-matrix","display_name":"Nonnegative matrix","score":0.6092737913131714},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5653753876686096},{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.492208868265152},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4662313461303711},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4585769474506378},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44489210844039917},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4421488046646118},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4207678735256195},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.2718448042869568},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2579303979873657},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18858784437179565},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.16288316249847412},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.05911475419998169}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8252376317977905},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.8000091314315796},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6337782144546509},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.6092737913131714},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5653753876686096},{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.492208868265152},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4662313461303711},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4585769474506378},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44489210844039917},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4421488046646118},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4207678735256195},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2718448042869568},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2579303979873657},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18858784437179565},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.16288316249847412},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.05911475419998169},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-013-9704-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-013-9704-0","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4699999988079071}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W72893484","https://openalex.org/W200590909","https://openalex.org/W598314002","https://openalex.org/W828079620","https://openalex.org/W1481438721","https://openalex.org/W1500921805","https://openalex.org/W1504685514","https://openalex.org/W1544013721","https://openalex.org/W1826624540","https://openalex.org/W1902027874","https://openalex.org/W1912120252","https://openalex.org/W1963657892","https://openalex.org/W1980642013","https://openalex.org/W2002120677","https://openalex.org/W2003234507","https://openalex.org/W2005300783","https://openalex.org/W2017246569","https://openalex.org/W2020953164","https://openalex.org/W2026978576","https://openalex.org/W2029803083","https://openalex.org/W2053479878","https://openalex.org/W2054749426","https://openalex.org/W2056242663","https://openalex.org/W2059745395","https://openalex.org/W2061781854","https://openalex.org/W2066019014","https://openalex.org/W2068066892","https://openalex.org/W2075665712","https://openalex.org/W2076566842","https://openalex.org/W2081494214","https://openalex.org/W2089079408","https://openalex.org/W2090611972","https://openalex.org/W2098098075","https://openalex.org/W2101196233","https://openalex.org/W2103339967","https://openalex.org/W2118718620","https://openalex.org/W2124172487","https://openalex.org/W2126210866","https://openalex.org/W2135029798","https://openalex.org/W2140318696","https://openalex.org/W2152557171","https://openalex.org/W2389044384","https://openalex.org/W2963053947","https://openalex.org/W3143596294","https://openalex.org/W4235739749","https://openalex.org/W4295016751","https://openalex.org/W4302087481"],"related_works":["https://openalex.org/W2088770317","https://openalex.org/W2012642013","https://openalex.org/W2166191203","https://openalex.org/W2991398534","https://openalex.org/W2165495021","https://openalex.org/W1845372869","https://openalex.org/W2091334405","https://openalex.org/W1511345785","https://openalex.org/W2017288758","https://openalex.org/W3099441337"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}