{"id":"https://openalex.org/W3007620966","doi":"https://doi.org/10.1137/19m1271750","title":"Novel Proximal Gradient Methods for Nonnegative Matrix Factorization with Sparsity Constraints","display_name":"Novel Proximal Gradient Methods for Nonnegative Matrix Factorization with Sparsity Constraints","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3007620966","doi":"https://doi.org/10.1137/19m1271750","mag":"3007620966"},"language":"en","primary_location":{"id":"doi:10.1137/19m1271750","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1271750","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","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/A5041397571","display_name":"Marc Teboulle","orcid":"https://orcid.org/0000-0002-4228-131X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marc Teboulle","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4228-131X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5038911688","display_name":"Yakov Vaisbourd","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yakov Vaisbourd","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0634,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.84726225,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"13","issue":"1","first_page":"381","last_page":"421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987000226974487,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"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/T10727","display_name":"Ultrasound Imaging and Elastography","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.8066474795341492},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6305651664733887},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5921376347541809},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5769884586334229},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5707210898399353},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5612390041351318},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.5044838190078735},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.49427103996276855},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4883961081504822},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.44083172082901},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.43314698338508606},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42679280042648315},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3983660042285919},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3588446378707886},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21968355774879456},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.15972644090652466},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.091275155544281},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08705994486808777}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.8066474795341492},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6305651664733887},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5921376347541809},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5769884586334229},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5707210898399353},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5612390041351318},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.5044838190078735},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.49427103996276855},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4883961081504822},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.44083172082901},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.43314698338508606},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42679280042648315},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3983660042285919},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3588446378707886},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21968355774879456},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.15972644090652466},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.091275155544281},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08705994486808777},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1271750","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1271750","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G948024957","display_name":null,"funder_award_id":"1844/16","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G964900516","display_name":null,"funder_award_id":"GIF-GI1253304-.6-2014","funder_id":"https://openalex.org/F4320320947","funder_display_name":"German-Israeli Foundation for Scientific Research and Development"}],"funders":[{"id":"https://openalex.org/F4320320947","display_name":"German-Israeli Foundation for Scientific Research and Development","ror":"https://ror.org/00tntzp09"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1540764732","https://openalex.org/W1902027874","https://openalex.org/W1967138577","https://openalex.org/W1994292689","https://openalex.org/W2021361347","https://openalex.org/W2022541060","https://openalex.org/W2026034143","https://openalex.org/W2027982384","https://openalex.org/W2033468335","https://openalex.org/W2059745395","https://openalex.org/W2076566842","https://openalex.org/W2078853581","https://openalex.org/W2091334405","https://openalex.org/W2093492509","https://openalex.org/W2108840817","https://openalex.org/W2110096996","https://openalex.org/W2113359929","https://openalex.org/W2124172487","https://openalex.org/W2129732816","https://openalex.org/W2132538571","https://openalex.org/W2132692097","https://openalex.org/W2136787567","https://openalex.org/W2155151262","https://openalex.org/W2165685007","https://openalex.org/W2549127690","https://openalex.org/W2551153860","https://openalex.org/W2777528688","https://openalex.org/W2963774283","https://openalex.org/W2963967579"],"related_works":["https://openalex.org/W2127243424","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"],"abstract_inverted_index":{"We":[0,18],"consider":[1,84],"the":[2,52,59,69,77,89,94,107,118,135,143,146],"nonnegative":[3],"matrix":[4],"factorization":[5],"(NMF)":[6],"problem":[7],"with":[8],"sparsity":[9,38],"constraints":[10],"formulated":[11],"as":[12],"a":[13,30,62],"nonconvex":[14],"composite":[15],"minimization":[16],"problem.":[17,91,109],"introduce":[19],"four":[20],"novel":[21,115],"proximal":[22,100],"gradient":[23,78],"based":[24,65],"algorithms":[25],"proven":[26],"globally":[27],"convergent":[28],"to":[29,37,50,132],"critical":[31],"point":[32],"and":[33,124],"which":[34],"are":[35,73,97,114],"applicable":[36],"constrained":[39],"NMF":[40,90,108],"models.":[41],"Our":[42],"approach":[43],"builds":[44],"on":[45],"recent":[46],"results":[47],"allowing":[48,130],"one":[49,131],"lift":[51],"classical":[53],"global":[54],"Lipschitz":[55,79],"continuity":[56,80],"requirement":[57],"through":[58],"use":[60],"of":[61,88,93,106,117,137,145],"non-Euclidean":[63,99],"Bregman":[64],"distance.":[66],"Since":[67],"under":[68],"proposed":[70,147],"framework":[71],"we":[72,82],"not":[74],"restricted":[75],"by":[76],"assumption,":[81],"can":[83],"new":[85],"decomposition":[86],"settings":[87],"Two":[92],"derived":[95],"schemes":[96,113],"genuine":[98],"methods":[101,121],"that":[102],"tackle":[103],"nonstandard":[104],"decompositions":[105],"The":[110],"two":[111],"other":[112],"extensions":[116],"well-known":[119],"state-of-the-art":[120],"(the":[122],"multiplicative":[123],"hierarchical":[125],"alternating":[126],"least":[127],"squares),":[128],"thus":[129],"significantly":[133],"broaden":[134],"scope":[136],"these":[138],"algorithms.":[139],"Numerical":[140],"experiments":[141],"illustrate":[142],"performance":[144],"methods.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}