{"id":"https://openalex.org/W2559085366","doi":"https://doi.org/10.48550/arxiv.1611.10041","title":"Subsampled online matrix factorization with convergence guarantees","display_name":"Subsampled online matrix factorization with convergence guarantees","publication_year":2016,"publication_date":"2016-11-30","ids":{"openalex":"https://openalex.org/W2559085366","doi":"https://doi.org/10.48550/arxiv.1611.10041","mag":"2559085366"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1611.10041","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.10041","pdf_url":"https://arxiv.org/pdf/1611.10041","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1611.10041","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061701877","display_name":"Arthur Mensch","orcid":"https://orcid.org/0000-0001-7866-0461","observed_orcids":["https://orcid.org/0000-0001-7866-0461"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mensch, Arthur","raw_affiliation_strings":["PARIETAL","Modelling brain structure, function and variability based on high-field MRI data"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PARIETAL","institution_ids":[]},{"raw_affiliation_string":"Modelling brain structure, function and variability based on high-field MRI data","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062817741","display_name":"Julien Mairal","orcid":"https://orcid.org/0000-0001-6991-2110","observed_orcids":["https://orcid.org/0000-0001-6991-2110"]},"institutions":[{"id":"https://openalex.org/I4405259482","display_name":"THOTH: Apprentissage de mod\u00e8les visuels \u00e0 partir de donn\u00e9es massives","ror":"https://ror.org/02a2awp29","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210101348","https://openalex.org/I4210149092","https://openalex.org/I4405259482","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mairal, Julien","raw_affiliation_strings":["LEAR","Apprentissage de mod\u00e8les \u00e0 partir de donn\u00e9es massives"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LEAR","institution_ids":[]},{"raw_affiliation_string":"Apprentissage de mod\u00e8les \u00e0 partir de donn\u00e9es massives","institution_ids":["https://openalex.org/I4405259482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074733625","display_name":"Gael P. Varoquaux","orcid":"https://orcid.org/0000-0003-1076-5122","observed_orcids":["https://orcid.org/0000-0003-1076-5122"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Varoquaux, Ga\u00ebl","raw_affiliation_strings":["PARIETAL","Modelling brain structure, function and variability based on high-field MRI data"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PARIETAL","institution_ids":[]},{"raw_affiliation_string":"Modelling brain structure, function and variability based on high-field MRI data","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026762833","display_name":"Bertrand Thirion","orcid":"https://orcid.org/0000-0001-5018-7895","observed_orcids":["https://orcid.org/0000-0001-5018-7895"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thirion, Bertrand","raw_affiliation_strings":["PARIETAL","Modelling brain structure, function and variability based on high-field MRI data","Service NEUROSPIN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PARIETAL","institution_ids":[]},{"raw_affiliation_string":"Modelling brain structure, function and variability based on high-field MRI data","institution_ids":[]},{"raw_affiliation_string":"Service NEUROSPIN","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9775000214576721,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9775000214576721,"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":0.008700000122189522,"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":0.005499999970197678,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subsampling","display_name":"subsampling","score":0.9670000076293945},{"id":"https://openalex.org/keywords/convergence-guarantees","display_name":"convergence guarantees","score":0.6940000057220459},{"id":"https://openalex.org/keywords/streaming-algorithms","display_name":"streaming algorithms","score":0.6439999938011169},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.5630000233650208},{"id":"https://openalex.org/keywords/high-dimensional-data","display_name":"high-dimensional data","score":0.628000020980835},{"id":"https://openalex.org/keywords/feature-redundancy","display_name":"feature redundancy","score":0.6200000047683716},{"id":"https://openalex.org/keywords/space-efficient-algorithms","display_name":"memory-efficient algorithms","score":0.5379999876022339}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6845037937164307},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6752756237983704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6079089045524597},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.46965447068214417},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4604940712451935},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.4525635838508606},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3148620128631592},{"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/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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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":3,"locations":[{"id":"pmh:oai:arXiv.org:1611.10041","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.10041","pdf_url":"https://arxiv.org/pdf/1611.10041","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01405058v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-01405058","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"NIPS Workshop on Optimization for Machine Learning, Dec 2016, Barcelone, Spain","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.48550/arxiv.1611.10041","doi":"https://doi.org/10.48550/arxiv.1611.10041","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1611.10041","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1611.10041","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.10041","pdf_url":"https://arxiv.org/pdf/1611.10041","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1791038712","https://openalex.org/W1974438823","https://openalex.org/W1975900269","https://openalex.org/W2105464873","https://openalex.org/W2107438106","https://openalex.org/W2112447569","https://openalex.org/W2117686388","https://openalex.org/W2135046866","https://openalex.org/W2143238292","https://openalex.org/W2950012781","https://openalex.org/W2952215077","https://openalex.org/W2962772219"],"related_works":["https://openalex.org/W2794559785","https://openalex.org/W2950631682","https://openalex.org/W2950281908","https://openalex.org/W1754499339","https://openalex.org/W2013873776","https://openalex.org/W2583828359","https://openalex.org/W3102011585","https://openalex.org/W2084977674","https://openalex.org/W1973739845","https://openalex.org/W119752240"],"abstract_inverted_index":{"We":[0,67],"present":[1,68],"a":[2,69,77],"matrix":[3,28,47],"factorization":[4,48],"algorithm":[5,25],"that":[6,11,18,72,93,103],"scales":[7],"to":[8,44,59,75,89,99],"input":[9],"matrices":[10],"are":[12],"large":[13],"in":[14,34,106],"both":[15],"dimensions":[16],"(i.e.,":[17],"contains":[19],"morethan":[20],"1TB":[21],"of":[22,80],"data).":[23],"The":[24],"streams":[26],"the":[27,61,81,100],"columns":[29],"while":[30],"subsampling":[31],"them,":[32],"resulting":[33],"low":[35],"complexity":[36],"per":[37],"iteration":[38],"andreasonable":[39],"memory":[40],"footprint.":[41],"In":[42],"contrast":[43],"previous":[45,90],"online":[46,91],"methods,":[49],"our":[50],"approach":[51],"relies":[52],"on":[53],"low-dimensional":[54],"statistics":[55],"from":[56],"past":[57],"iterates":[58],"control":[60],"extra":[62],"variance":[63],"introduced":[64],"by":[65],"subsampling.":[66],"convergence":[70],"analysis":[71],"guarantees":[73],"us":[74],"reach":[76],"stationary":[78],"point":[79],"problem.":[82],"Large":[83],"speed-ups":[84],"can":[85],"be":[86],"obtained":[87],"compared":[88],"algorithms":[92],"do":[94],"not":[95],"perform":[96],"subsampling,":[97],"thanks":[98],"feature":[101],"redundancy":[102],"often":[104],"exists":[105],"high-dimensional":[107],"settings.":[108]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}
