{"id":"https://openalex.org/W2235103357","doi":"https://doi.org/10.1007/978-3-642-21735-7_31","title":"Kullback-Leibler Divergence for Nonnegative Matrix Factorization","display_name":"Kullback-Leibler Divergence for Nonnegative Matrix Factorization","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2235103357","doi":"https://doi.org/10.1007/978-3-642-21735-7_31","mag":"2235103357"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-21735-7_31","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"book series"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"book-chapter","type_crossref":"book-chapter","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/A5080414124","display_name":"Zhirong Yang","orcid":"https://orcid.org/0000-0001-8412-5684"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"funder","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Zhirong Yang","raw_affiliation_strings":["Department of Information and Computer Science, Aalto University, P.O.Box 15400, FI-00076, Espoo, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Science, Aalto University, P.O.Box 15400, FI-00076, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100420147","display_name":"He Zhang","orcid":"https://orcid.org/0000-0003-2304-9387"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"funder","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"He Zhang","raw_affiliation_strings":["Department of Information and Computer Science, Aalto University, P.O.Box 15400, FI-00076, Espoo, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Science, Aalto University, P.O.Box 15400, FI-00076, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108617666","display_name":"Zhijian Yuan","orcid":null},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"funder","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Zhijian Yuan","raw_affiliation_strings":["Department of Information and Computer Science, Aalto University, P.O.Box 15400, FI-00076, Espoo, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Science, Aalto University, P.O.Box 15400, FI-00076, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085424325","display_name":"Erkki Oja","orcid":null},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"funder","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Erkki Oja","raw_affiliation_strings":["Department of Information and Computer Science, Aalto University, P.O.Box 15400, FI-00076, Espoo, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Science, Aalto University, P.O.Box 15400, FI-00076, Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":4.809,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.989556,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"250","last_page":"257"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9988,"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"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9988,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987,"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/T10057","display_name":"Face and Expression Recognition","score":0.9983,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative Matrix Factorization","score":0.872517},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.79133},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.7751161},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization","score":0.76430166}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.872517},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.79133},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.7751161},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.76430166},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5955759},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5341275},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.50879747},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.47715348},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4579957},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42070836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36728048},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32881457},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29772532},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.15934077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08337718},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-21735-7_31","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"book series"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":20,"referenced_works":["https://openalex.org/W1246381107","https://openalex.org/W1902027874","https://openalex.org/W1999935624","https://openalex.org/W2039844283","https://openalex.org/W2051237043","https://openalex.org/W2059745395","https://openalex.org/W2076566842","https://openalex.org/W2085937140","https://openalex.org/W2110096996","https://openalex.org/W2132538571","https://openalex.org/W2135029798","https://openalex.org/W2144750001","https://openalex.org/W2168446235","https://openalex.org/W2187089797","https://openalex.org/W2404400936","https://openalex.org/W2990138404","https://openalex.org/W2999905431","https://openalex.org/W3143596294","https://openalex.org/W4251143728","https://openalex.org/W88153722"],"related_works":["https://openalex.org/W4390394189","https://openalex.org/W2972997031","https://openalex.org/W2792706544","https://openalex.org/W2539013788","https://openalex.org/W2156699640","https://openalex.org/W2146544734","https://openalex.org/W2127243424","https://openalex.org/W2045265907","https://openalex.org/W2037504162","https://openalex.org/W1568451138"],"abstract_inverted_index":null,"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2235103357","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-04-15T18:12:42.106195","created_date":"2016-06-24"}