{"id":"https://openalex.org/W2902258842","doi":"https://doi.org/10.1109/rtsi.2018.8548361","title":"Parallelization of the Hierarchical Alternating Least Squares Algorithm for Nonnegative Matrix Factorization","display_name":"Parallelization of the Hierarchical Alternating Least Squares Algorithm for Nonnegative Matrix Factorization","publication_year":2018,"publication_date":"2018-09-01","ids":{"openalex":"https://openalex.org/W2902258842","doi":"https://doi.org/10.1109/rtsi.2018.8548361","mag":"2902258842"},"language":"en","primary_location":{"id":"doi:10.1109/rtsi.2018.8548361","is_oa":false,"landing_page_url":"https://doi.org/10.1109/rtsi.2018.8548361","pdf_url":null,"source":{"id":"https://openalex.org/S4306498310","display_name":"2018 IEEE 4th International Forum on Research and Technology for Society and Industry (RTSI)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE 4th International Forum on Research and Technology for Society and Industry (RTSI)","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/A5085161522","display_name":"Markus Flatz","orcid":null},"institutions":[{"id":"https://openalex.org/I182212641","display_name":"University of Salzburg","ror":"https://ror.org/05gs8cd61","country_code":"AT","type":"education","lineage":["https://openalex.org/I182212641"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Markus Flatz","raw_affiliation_strings":["Department of Computer Sciences, University of Salzburg, Salzburg, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, University of Salzburg, Salzburg, Austria","institution_ids":["https://openalex.org/I182212641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027207015","display_name":"Rade Kutil","orcid":"https://orcid.org/0000-0003-4805-1096"},"institutions":[{"id":"https://openalex.org/I182212641","display_name":"University of Salzburg","ror":"https://ror.org/05gs8cd61","country_code":"AT","type":"education","lineage":["https://openalex.org/I182212641"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Rade Kutil","raw_affiliation_strings":["Department of Computer Sciences, University of Salzburg, Salzburg, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, University of Salzburg, Salzburg, Austria","institution_ids":["https://openalex.org/I182212641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022662194","display_name":"Mari\u00e1n Vajter\u0161ic","orcid":null},"institutions":[{"id":"https://openalex.org/I182212641","display_name":"University of Salzburg","ror":"https://ror.org/05gs8cd61","country_code":"AT","type":"education","lineage":["https://openalex.org/I182212641"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Marian Vajtersic","raw_affiliation_strings":["Department of Computer Sciences, University of Salzburg, Salzburg, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, University of Salzburg, Salzburg, Austria","institution_ids":["https://openalex.org/I182212641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085161522"],"corresponding_institution_ids":["https://openalex.org/I182212641"],"apc_list":null,"apc_paid":null,"fwci":0.2019,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56208474,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"401","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9932000041007996,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9932000041007996,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9896000027656555,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9814000129699707,"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":0.7739965319633484},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5893087983131409},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5696298480033875},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.5572147965431213},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5460013747215271},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5027656555175781},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.49492305517196655},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4874894618988037},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.48470258712768555},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4624977111816406},{"id":"https://openalex.org/keywords/row-and-column-spaces","display_name":"Row and column spaces","score":0.4456685483455658},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.44241371750831604},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4113801121711731},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4091103672981262},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3508276641368866}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.7739965319633484},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5893087983131409},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5696298480033875},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.5572147965431213},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5460013747215271},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5027656555175781},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.49492305517196655},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4874894618988037},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.48470258712768555},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4624977111816406},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.4456685483455658},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.44241371750831604},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4113801121711731},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4091103672981262},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3508276641368866},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/rtsi.2018.8548361","is_oa":false,"landing_page_url":"https://doi.org/10.1109/rtsi.2018.8548361","pdf_url":null,"source":{"id":"https://openalex.org/S4306498310","display_name":"2018 IEEE 4th International Forum on Research and Technology for Society and Industry (RTSI)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE 4th International Forum on Research and Technology for Society and Industry (RTSI)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W206759535","https://openalex.org/W1491548974","https://openalex.org/W1594523130","https://openalex.org/W1692592558","https://openalex.org/W1902027874","https://openalex.org/W2013029404","https://openalex.org/W2017288758","https://openalex.org/W2059745395","https://openalex.org/W2061631122","https://openalex.org/W2075222291","https://openalex.org/W2075665712","https://openalex.org/W2076566842","https://openalex.org/W2092423825","https://openalex.org/W2093492509","https://openalex.org/W2098098075","https://openalex.org/W2110096996","https://openalex.org/W2112988892","https://openalex.org/W2113359929","https://openalex.org/W2124890708","https://openalex.org/W2132692097","https://openalex.org/W2136787567","https://openalex.org/W2142621404","https://openalex.org/W2144351558","https://openalex.org/W2285339552","https://openalex.org/W2519301224","https://openalex.org/W2523548419","https://openalex.org/W2789406368","https://openalex.org/W4237234927","https://openalex.org/W6608466485","https://openalex.org/W6695757358"],"related_works":["https://openalex.org/W90906771","https://openalex.org/W2018828772","https://openalex.org/W2529185025","https://openalex.org/W2809723425","https://openalex.org/W2052708136","https://openalex.org/W2005302727","https://openalex.org/W2146369775","https://openalex.org/W1966476169","https://openalex.org/W1533938001","https://openalex.org/W2100452915"],"abstract_inverted_index":{"The":[0,45],"Nonnegative":[1,84],"Matrix":[2],"Factorization":[3],"(NMF)":[4],"approximates":[5],"a":[6,11,94,125],"large":[7],"nonnegative":[8,17],"matrix":[9,101],"as":[10],"product":[12],"of":[13,20,23,28,63,71,99],"two":[14,41],"significantly":[15],"smaller":[16],"matrices.":[18],"Because":[19],"the":[21,24,30,40,53,64,74,105,154],"nonconvexity":[22],"constrained":[25],"optimization":[26],"problem":[27],"finding":[29],"best":[31,65],"approximation,":[32],"all":[33],"current":[34],"algorithms":[35,66,88],"are":[36,146],"iterative":[37],"and":[38,103,107,133,142],"optimize":[39],"factor":[42],"matrices":[43],"alternatingly.":[44],"resulting":[46],"sublinear":[47],"convergence":[48,72],"rates":[49],"give":[50],"rise":[51],"to":[52,92,120,129,139,150,153],"demand":[54],"for":[55,67,137],"parallel":[56],"implementations":[57],"on":[58],"high":[59],"performance":[60],"computers.":[61],"One":[62],"NMF":[68],"in":[69,110,148],"terms":[70],"is":[73,117],"Hierarchical":[75],"Alternating":[76,83],"Least":[77,85],"Squares":[78,86],"(HALS)":[79],"algorithm.":[80],"While":[81],"other":[82],"(ANLS)":[87],"have":[89,93],"been":[90,162],"shown":[91],"rather":[95],"straight-forward":[96],"parallelization":[97,126],"because":[98],"independent":[100],"rows":[102],"columns,":[104],"row":[106],"column":[108],"updates":[109],"HALS":[111,159],"must":[112],"be":[113],"strictly":[114],"consecutive,":[115],"which":[116],"more":[118],"difficult":[119],"parallelize.":[121],"We":[122],"show":[123],"that":[124],"strategy":[127],"similar":[128],"ANLS":[130],"parallelizations":[131],"exists":[132],"yields":[134],"good":[135],"speedups":[136],"up":[138],"64":[140],"processes":[141],"satisfactory":[143],"beyond.":[144],"These":[145],"competitive":[147],"comparison":[149],"previous":[151],"solutions":[152],"problem.":[155],"To":[156],"our":[157],"knowledge,":[158],"has":[160],"not":[161],"parallelized":[163],"before.":[164]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
