{"id":"https://openalex.org/W3039227585","doi":"https://doi.org/10.1109/civemsa48639.2020.9132972","title":"On Approximating the Non-negative Rank: Applications to Unsupervised Image Reduction","display_name":"On Approximating the Non-negative Rank: Applications to Unsupervised Image Reduction","publication_year":2020,"publication_date":"2020-06-01","ids":{"openalex":"https://openalex.org/W3039227585","doi":"https://doi.org/10.1109/civemsa48639.2020.9132972","mag":"3039227585"},"language":"en","primary_location":{"id":"doi:10.1109/civemsa48639.2020.9132972","is_oa":false,"landing_page_url":"https://doi.org/10.1109/civemsa48639.2020.9132972","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE International Conference on Computational Intelligence and Virtual Environments for Measurement Systems and Applications (CIVEMSA)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2434/724574","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018303936","display_name":"Mohanad Abukmeil","orcid":null},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Mohanad Abukmeil","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063632316","display_name":"Stefano Ferrari","orcid":"https://orcid.org/0000-0002-4982-6212"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Ferrari","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031772222","display_name":"Angelo Genovese","orcid":"https://orcid.org/0000-0002-3683-4723"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Angelo Genovese","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009147954","display_name":"Vincenzo Piuri","orcid":"https://orcid.org/0000-0003-3178-8198"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Vincenzo Piuri","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004969615","display_name":"Fabio Scotti","orcid":"https://orcid.org/0000-0002-4277-3701"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fabio Scotti","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 degli Studi di Milano, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I189158943"],"apc_list":null,"apc_paid":null,"fwci":0.1709,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.4526363,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9983000159263611,"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":0.9983000159263611,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9983000159263611,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.8047980070114136},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.7077997326850891},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6644673943519592},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6626096963882446},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.6385174989700317},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6123843789100647},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5414599776268005},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5381549000740051},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5376983284950256},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.48790785670280457},{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"Unsupervised learning","score":0.4555673599243164},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.45482802391052246},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3866863250732422},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3254830837249756},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2104995846748352},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10051366686820984},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09298253059387207}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.8047980070114136},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.7077997326850891},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6644673943519592},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6626096963882446},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.6385174989700317},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6123843789100647},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5414599776268005},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5381549000740051},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5376983284950256},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.48790785670280457},{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.4555673599243164},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.45482802391052246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3866863250732422},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3254830837249756},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2104995846748352},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10051366686820984},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09298253059387207},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/civemsa48639.2020.9132972","is_oa":false,"landing_page_url":"https://doi.org/10.1109/civemsa48639.2020.9132972","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE International Conference on Computational Intelligence and Virtual Environments for Measurement Systems and Applications (CIVEMSA)","raw_type":"proceedings-article"},{"id":"pmh:oai:air.unimi.it:2434/724574","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/724574","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/bookPart"}],"best_oa_location":{"id":"pmh:oai:air.unimi.it:2434/724574","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/724574","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/bookPart"},"sustainable_development_goals":[{"score":0.5600000023841858,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1507780841","https://openalex.org/W1576369095","https://openalex.org/W1702933071","https://openalex.org/W1736726159","https://openalex.org/W1854811422","https://openalex.org/W1902027874","https://openalex.org/W2007339694","https://openalex.org/W2013912476","https://openalex.org/W2039844283","https://openalex.org/W2048695508","https://openalex.org/W2118550318","https://openalex.org/W2118858186","https://openalex.org/W2132164018","https://openalex.org/W2133665775","https://openalex.org/W2618107892","https://openalex.org/W2750384547","https://openalex.org/W2784470426","https://openalex.org/W2810443465","https://openalex.org/W2823336313","https://openalex.org/W2946300279","https://openalex.org/W2947000318","https://openalex.org/W2963847595","https://openalex.org/W2970158413","https://openalex.org/W3128588266","https://openalex.org/W4226065182","https://openalex.org/W4283268983","https://openalex.org/W4288616989","https://openalex.org/W6637458550","https://openalex.org/W6639041367","https://openalex.org/W6677919164","https://openalex.org/W6743688258","https://openalex.org/W6758555458"],"related_works":["https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2539013788","https://openalex.org/W2792706544","https://openalex.org/W1568451138","https://openalex.org/W2156699640","https://openalex.org/W2045265907","https://openalex.org/W2972997031","https://openalex.org/W34555840","https://openalex.org/W4294224199"],"abstract_inverted_index":{"Unsupervised":[0],"Learning":[1],"(UL)":[2],"methods":[3],"are":[4],"a":[5,112,122],"class":[6],"of":[7,42,72,91,156],"machine":[8],"learning":[9],"which":[10],"aims":[11],"to":[12,81,87,114,131],"disentangle":[13],"the":[14,18,21,31,37,46,49,56,64,73,78,83,89,92,95,105,117,126,146,154],"representations":[15,57],"and":[16,52,61,102,136],"reduce":[17],"dimensionality":[19,90],"among":[20,141],"data":[22,38,151],"without":[23],"any":[24],"predefined":[25],"labels.":[26],"Among":[27],"all":[28],"UL":[29],"methods,":[30],"Non-negative":[32],"Matrix":[33],"Factorization":[34],"(NMF)":[35],"factorizes":[36],"into":[39],"two":[40],"subspaces":[41],"non-negative":[43,106,127],"components.":[44],"Moreover,":[45],"NMF":[47,79],"enforces":[48],"non-negativity,":[50],"sparsity,":[51],"part-based":[53],"analysis,":[54],"thus":[55],"can":[58],"be":[59],"interpreted":[60],"explained":[62],"for":[63,125],"Explainable":[65],"Artificial":[66],"Intelligence":[67],"(XAI)":[68],"applications.":[69],"However,":[70],"one":[71],"main":[74],"issues":[75],"when":[76],"using":[77],"is":[80,97,109],"impose":[82],"factorization":[84],"rank":[85,96,107,128],"r":[86,129],"identify":[88],"subspaces,":[93],"where":[94],"usually":[98],"unknown":[99],"in":[100],"advance":[101],"known":[103],"as":[104,111],"that":[108],"used":[110],"prior":[113],"carrying":[115],"out":[116],"factorization.":[118],"Accordingly,":[119],"we":[120,137],"propose":[121],"novel":[123],"method":[124,140],"approximation":[130],"help":[132],"solving":[133],"this":[134],"problem,":[135],"generalize":[138],"our":[139,157],"different":[142,149],"image":[143,150],"scales.":[144],"Where,":[145],"results":[147],"on":[148],"sets":[152],"confirm":[153],"validity":[155],"approach.":[158]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}