{"id":"https://openalex.org/W2144920235","doi":"https://doi.org/10.1145/1102351.1102451","title":"Non-negative tensor factorization with applications to statistics and computer vision","display_name":"Non-negative tensor factorization with applications to statistics and computer vision","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2144920235","doi":"https://doi.org/10.1145/1102351.1102451","mag":"2144920235"},"language":"en","primary_location":{"id":"doi:10.1145/1102351.1102451","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1102351.1102451","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 22nd international conference on Machine learning - ICML '05","raw_type":"proceedings-article"},"type":"conference-paper","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/A5075004917","display_name":"Amnon Shashua","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Amnon Shashua","raw_affiliation_strings":["The Hebrew University of Jerusalem, Jerusalem, Israel","The Hebrew University of Jerusalem , Jerusalem , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"The Hebrew University of Jerusalem , Jerusalem , Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000106487","display_name":"Tamir Hazan","orcid":"https://orcid.org/0000-0003-1652-3845"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Tamir Hazan","raw_affiliation_strings":["The Hebrew University of Jerusalem, Jerusalem, Israel","The Hebrew University of Jerusalem , Jerusalem , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"The Hebrew University of Jerusalem , Jerusalem , Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":4.1555,"has_fulltext":false,"cited_by_count":508,"citation_normalized_percentile":{"value":0.96296296,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"792","last_page":"799"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9919000267982483,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9807999730110168,"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":0.6913402676582336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6096993684768677},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.6028162240982056},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5813336968421936},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5377033352851868},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.47905978560447693},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4721536636352539},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4444020688533783},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4204232096672058},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3982675075531006},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3494618535041809},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3247417211532593},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12160462141036987},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.07525634765625}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.6913402676582336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6096993684768677},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6028162240982056},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5813336968421936},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5377033352851868},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.47905978560447693},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4721536636352539},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4444020688533783},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4204232096672058},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3982675075531006},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3494618535041809},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3247417211532593},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12160462141036987},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.07525634765625},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1102351.1102451","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1102351.1102451","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 22nd international conference on Machine learning - ICML '05","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.76.5775","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.76.5775","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.huji.ac.il/~shashua/papers/NTF-icml.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.97.7293","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.97.7293","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.huji.ac.il/~tamirr/papers/NTF-icml05.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W72893484","https://openalex.org/W1544729927","https://openalex.org/W1612003148","https://openalex.org/W1680583314","https://openalex.org/W1902027874","https://openalex.org/W2002598080","https://openalex.org/W2013912476","https://openalex.org/W2049633694","https://openalex.org/W2053197265","https://openalex.org/W2057503509","https://openalex.org/W2059745395","https://openalex.org/W2066808305","https://openalex.org/W2073502026","https://openalex.org/W2090799283","https://openalex.org/W2111448058","https://openalex.org/W2113055885","https://openalex.org/W2121739212","https://openalex.org/W2125027820","https://openalex.org/W2138996475","https://openalex.org/W2140318696","https://openalex.org/W2147152072","https://openalex.org/W2150059498","https://openalex.org/W2396960496","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2127243424","https://openalex.org/W2037504162","https://openalex.org/W4390394189","https://openalex.org/W2792706544","https://openalex.org/W1568451138","https://openalex.org/W2539013788","https://openalex.org/W2156699640","https://openalex.org/W2045265907","https://openalex.org/W2972997031","https://openalex.org/W2075222291"],"abstract_inverted_index":{"We":[0,26,58],"derive":[1,59],"algorithms":[2],"for":[3],"finding":[4],"a":[5,19,60],"non-negative":[6,14],"n-dimensional":[7],"tensor":[8],"factorization":[9,16],"(n-NTF)":[10],"which":[11],"includes":[12],"the":[13,28],"matrix":[15],"(NMF)":[17],"as":[18],"particular":[20],"case":[21],"when":[22],"n":[23],"=":[24],"2.":[25],"motivate":[27],"use":[29],"of":[30,35],"n-NTF":[31],"in":[32,44,50],"three":[33],"areas":[34],"data":[36],"analysis:":[37],"(i)":[38],"connection":[39],"to":[40],"latent":[41],"class":[42],"models":[43],"statistics,":[45],"(ii)":[46],"sparse":[47],"image":[48],"coding":[49],"computer":[51],"vision,":[52],"and":[53,66],"(iii)":[54],"model":[55],"selection":[56],"problems.":[57,75],"\"direct\"":[61],"positive-preserving":[62],"gradient":[63],"descent":[64],"algorithm":[65],"an":[67],"alternating":[68],"scheme":[69],"based":[70],"on":[71],"repeated":[72],"multiple":[73],"rank-1":[74]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":30},{"year":2020,"cited_by_count":38},{"year":2019,"cited_by_count":35},{"year":2018,"cited_by_count":37},{"year":2017,"cited_by_count":25},{"year":2016,"cited_by_count":36},{"year":2015,"cited_by_count":28},{"year":2014,"cited_by_count":30},{"year":2013,"cited_by_count":28},{"year":2012,"cited_by_count":26}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}