{"id":"https://openalex.org/W2976760214","doi":"https://doi.org/10.1109/isit.2019.8849441","title":"Non-Negative Matrix Factorization via Low-Rank Stochastic Manifold Optimization","display_name":"Non-Negative Matrix Factorization via Low-Rank Stochastic Manifold Optimization","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2976760214","doi":"https://doi.org/10.1109/isit.2019.8849441","mag":"2976760214"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2019.8849441","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849441","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5018239741","display_name":"Ahmed Douik","orcid":"https://orcid.org/0000-0001-7791-9443"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ahmed Douik","raw_affiliation_strings":["California Institute of Technology (Caltech), California, United States of America"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology (Caltech), California, United States of America","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002430773","display_name":"Babak Hassibi","orcid":"https://orcid.org/0000-0002-1375-5838"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Babak Hassibi","raw_affiliation_strings":["California Institute of Technology (Caltech), California, United States of America"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology (Caltech), California, United States of America","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018239741"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10306126,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"497","last_page":"501"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9993000030517578,"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":0.9993000030517578,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9952999949455261,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9940000176429749,"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/matrix-decomposition","display_name":"Matrix decomposition","score":0.6404265761375427},{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.5876172780990601},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5451944470405579},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5248608589172363},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.520110011100769},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4514238238334656},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.4427153170108795},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4404307007789612},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43055230379104614},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4005725681781769},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2761915326118469},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20644527673721313},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15975919365882874},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14224258065223694},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0810210108757019},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.07585868239402771}],"concepts":[{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6404265761375427},{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.5876172780990601},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5451944470405579},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5248608589172363},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.520110011100769},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4514238238334656},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.4427153170108795},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4404307007789612},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43055230379104614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4005725681781769},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2761915326118469},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20644527673721313},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15975919365882874},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14224258065223694},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0810210108757019},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.07585868239402771},{"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/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/isit.2019.8849441","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849441","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:authors.library.caltech.edu:112853","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20220112-76592900","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"},{"id":"pmh:oai:authors.library.caltech.edu:99072","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20191004-100332012","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1706897027","https://openalex.org/W1804110266","https://openalex.org/W1854811422","https://openalex.org/W2042182457","https://openalex.org/W2103560185","https://openalex.org/W2108840817","https://openalex.org/W2135029798","https://openalex.org/W2144313459","https://openalex.org/W2161997479","https://openalex.org/W2211574168","https://openalex.org/W2509988436","https://openalex.org/W2515212212","https://openalex.org/W2541338223","https://openalex.org/W2786130756","https://openalex.org/W2804284765","https://openalex.org/W2889305943","https://openalex.org/W2962999825","https://openalex.org/W2963929357","https://openalex.org/W3098370332","https://openalex.org/W3122703110","https://openalex.org/W3143596294","https://openalex.org/W4205293427","https://openalex.org/W4298393077","https://openalex.org/W6639041367","https://openalex.org/W6680012447","https://openalex.org/W6681550237","https://openalex.org/W6683906321","https://openalex.org/W6688171335","https://openalex.org/W6717724730","https://openalex.org/W6728665592","https://openalex.org/W6748190050","https://openalex.org/W6751674073"],"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/W2146544734"],"abstract_inverted_index":{"Several":[0],"real-world":[1,138],"applications,":[2],"notably":[3],"in":[4,102,155],"non-negative":[5],"matrix":[6],"factorization,":[7],"graph-based":[8],"clustering,":[9],"and":[10,24,63,79,88,97,112,139],"machine":[11],"learning,":[12],"require":[13],"solving":[14,70],"a":[15,41,65,126],"convex":[16],"optimization":[17,67,71,107,123],"problem":[18,49],"over":[19],"the":[20,36,48,54,74,90,93,98,117,120],"set":[21,75],"of":[22,31,53,76,92,113,157],"stochastic":[23,26,78,81,95,100],"doubly":[25,80,99],"matrices.":[27,82],"A":[28],"common":[29],"feature":[30],"these":[32],"problems":[33,72],"is":[34,39,132,151],"that":[35],"optimal":[37],"solution":[38],"generally":[40],"low-rank":[42,55,77,94],"matrix.":[43],"This":[44],"paper":[45,86],"suggests":[46],"reformulating":[47],"by":[50],"taking":[51],"advantage":[52],"factorization":[56],"X":[57],"=":[58],"UV":[59],"<sup":[60],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[61],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">T</sup>":[62],"develops":[64],"Riemannian":[66,122],"framework":[68,124],"for":[69,142,162],"on":[73,137],"In":[83],"particular,":[84],"this":[85],"introduces":[87],"studies":[89],"geometry":[91],"multinomial":[96],"manifold":[101],"order":[103],"to":[104,153],"derive":[105],"first-order":[106],"algorithms.":[108],"Being":[109],"carefully":[110],"designed":[111],"lower":[114],"dimension":[115],"than":[116],"original":[118],"problem,":[119],"proposed":[121,149],"presents":[125],"clear":[127],"complexity":[128],"advantage.":[129],"The":[130,148],"claim":[131],"attested":[133],"through":[134],"numerical":[135],"experiments":[136],"synthetic":[140],"data":[141],"Non-negative":[143],"Matrix":[144],"Factorization":[145],"(NFM)":[146],"applications.":[147],"algorithm":[150],"shown":[152],"outperform,":[154],"terms":[156],"running":[158],"time,":[159],"state-of-the-art":[160],"methods":[161],"NFM.":[163]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}