{"id":"https://openalex.org/W2947854252","doi":"https://doi.org/10.1137/17m1116787","title":"Riemannian Stochastic Variance Reduced Gradient Algorithm with Retraction and Vector Transport","display_name":"Riemannian Stochastic Variance Reduced Gradient Algorithm with Retraction and Vector Transport","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2947854252","doi":"https://doi.org/10.1137/17m1116787","mag":"2947854252"},"language":"en","primary_location":{"id":"doi:10.1137/17m1116787","doi":"https://doi.org/10.1137/17m1116787","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1116787","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-140","russia-white-list-1"],"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 Optimization","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1702.05594","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025164609","display_name":"Hiroyuki Sato","orcid":"https://orcid.org/0000-0003-1399-8140","observed_orcids":["https://orcid.org/0000-0003-1399-8140"]},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroyuki Sato","raw_affiliation_strings":["Department of Applied Mathematics and Physics, Kyoto University, Kyoto, Japan"],"raw_orcid":"https://orcid.org/0000-0003-1399-8140","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Physics, Kyoto University, Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079080816","display_name":"Hiroyuki Kasai","orcid":"https://orcid.org/0000-0003-1161-6823","observed_orcids":["https://orcid.org/0000-0003-1161-6823"]},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroyuki Kasai","raw_affiliation_strings":["Graduate School of Informatics and Engineering, The University of Electro-Communications, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Informatics and Engineering, The University of Electro-Communications, Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023551959","display_name":"Bamdev Mishra","orcid":"https://orcid.org/0000-0001-7430-2843","observed_orcids":["https://orcid.org/0000-0001-7430-2843"]},"institutions":[{"id":"https://openalex.org/I4210162141","display_name":"Microsoft (India)","ror":"https://ror.org/04ww0w091","country_code":"IN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210162141"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Bamdev Mishra","raw_affiliation_strings":["Microsoft, Hyderabad, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft, Hyderabad, India","institution_ids":["https://openalex.org/I4210162141"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.93,"has_fulltext":true,"cited_by_count":95,"citation_normalized_percentile":{"value":0.96062129,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"29","issue":"2","first_page":"1444","last_page":"1472"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9639000296592712,"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":0.9639000296592712,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.013100000098347664,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.00860000029206276,"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/stochastic-variance-reduction","display_name":"stochastic variance reduction","score":0.765999972820282},{"id":"https://openalex.org/keywords/retraction","display_name":"retraction","score":0.8130000233650208},{"id":"https://openalex.org/keywords/vector-transport","display_name":"vector transport","score":0.9990000128746033},{"id":"https://openalex.org/keywords/riemannian-optimization","display_name":"Riemannian optimization","score":0.9110000133514404},{"id":"https://openalex.org/keywords/manifold-optimization","display_name":"manifold optimization","score":0.6330000162124634},{"id":"https://openalex.org/keywords/global-convergence","display_name":"global convergence","score":0.5960000157356262},{"id":"https://openalex.org/keywords/local-convergence-rate","display_name":"local convergence rate","score":0.9610000252723694},{"id":"https://openalex.org/keywords/symmetric-positive-definite-manifold","display_name":"symmetric positive definite manifold","score":0.9890000224113464},{"id":"https://openalex.org/keywords/grassmannians","display_name":"Grassmannians","score":0.9549999833106995},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"principal component analysis","score":0.9760000109672546},{"id":"https://openalex.org/keywords/low-rank-matrix-completion","display_name":"low-rank matrix completion","score":1.0}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8207968473434448},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.7076495885848999},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5627350807189941},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5462110638618469},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4944417476654053},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4727284014225006},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.46795880794525146},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.43800121545791626},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.43592405319213867},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4211563169956207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41827428340911865},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3381290137767792},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.20408138632774353},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16436916589736938},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11487376689910889},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0990724265575409},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08359819650650024},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1116787","doi":"https://doi.org/10.1137/17m1116787","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1116787","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-140","russia-white-list-1"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1702.05594","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.05594","pdf_url":"https://arxiv.org/pdf/1702.05594","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":"mag:2594807935","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1702.05594","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1702.05594","doi":"https://doi.org/10.48550/arxiv.1702.05594","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1702.05594","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":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1702.05594","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.05594","pdf_url":"https://arxiv.org/pdf/1702.05594","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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1738007175","display_name":"Riemannian optimization and applications for high-dimensional large-scale  data","funder_award_id":"16K00031","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8042317969","display_name":"Development of Riemannian conjugate gradient methods and their applications to large-scale problems","funder_award_id":"16K17647","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320323365","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2947854252.pdf","grobid_xml":"https://content.openalex.org/works/W2947854252.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W191817552","https://openalex.org/W1523661875","https://openalex.org/W1556236121","https://openalex.org/W1628278711","https://openalex.org/W1804110266","https://openalex.org/W1813021177","https://openalex.org/W1890144115","https://openalex.org/W1939652453","https://openalex.org/W1974766144","https://openalex.org/W1983496390","https://openalex.org/W1996267928","https://openalex.org/W2047152541","https://openalex.org/W2081962379","https://openalex.org/W2103096501","https://openalex.org/W2105875671","https://openalex.org/W2107438106","https://openalex.org/W2117354486","https://openalex.org/W2120717492","https://openalex.org/W2138674039","https://openalex.org/W2143915825","https://openalex.org/W2151358751","https://openalex.org/W2167623372","https://openalex.org/W2205007824","https://openalex.org/W2280254565","https://openalex.org/W2301983558","https://openalex.org/W2304667012","https://openalex.org/W2396329851","https://openalex.org/W2462905479","https://openalex.org/W2549348365","https://openalex.org/W2598524690","https://openalex.org/W2886593263","https://openalex.org/W2952215077","https://openalex.org/W2952594493","https://openalex.org/W2962851402","https://openalex.org/W2963901142","https://openalex.org/W3037096902","https://openalex.org/W4213452534"],"related_works":["https://openalex.org/W2594807935","https://openalex.org/W2396329851","https://openalex.org/W2598524690","https://openalex.org/W2620326289","https://openalex.org/W2138674039","https://openalex.org/W2549348365","https://openalex.org/W3199619927","https://openalex.org/W2399142700","https://openalex.org/W4390886626","https://openalex.org/W3092878522"],"abstract_inverted_index":{"In":[0,94],"recent":[1],"years,":[2],"stochastic":[3,34,143],"variance":[4,35],"reduction":[5],"algorithms":[6],"have":[7],"attracted":[8],"considerable":[9],"attention":[10],"for":[11],"minimizing":[12],"the":[13,32,63,96,102,106,110,119,129,136,140],"average":[14],"of":[15,21,31,48,105],"a":[16,27,41,68,73,80,86],"large":[17],"but":[18],"finite":[19],"number":[20],"loss":[22],"functions.":[23],"This":[24],"paper":[25],"proposes":[26],"novel":[28],"Riemannian":[29,107,142],"extension":[30],"Euclidean":[33],"reduced":[36],"gradient":[37,144],"(R-SVRG)":[38],"algorithm":[39,98,138,146],"to":[40,101],"manifold":[42,115],"search":[43],"space.":[44],"The":[45,132],"key":[46],"challenges":[47],"averaging,":[49],"adding,":[50],"and":[51,59,123],"subtracting":[52],"multiple":[53],"gradients":[54],"are":[55],"addressed":[56],"with":[57,72,85],"retraction":[58],"vector":[60],"transport.":[61],"For":[62],"proposed":[64,97,137],"algorithm,":[65],"we":[66],"present":[67],"global":[69],"convergence":[70,82],"analysis":[71,84,122],"decaying":[74],"step":[75,88],"size":[76,89],"as":[77,79,116,118],"well":[78,117],"local":[81],"rate":[83],"fixed":[87],"under":[90],"some":[91],"natural":[92],"assumptions.":[93],"addition,":[95],"is":[99],"applied":[100],"computation":[103],"problem":[104],"centroid":[108],"on":[109,128],"symmetric":[111],"positive":[112],"definite":[113],"(SPD)":[114],"principal":[120],"component":[121],"low-rank":[124],"matrix":[125],"completion":[126],"problems":[127],"Grassmann":[130],"manifold.":[131],"results":[133],"show":[134],"that":[135],"outperforms":[139],"standard":[141],"descent":[145],"in":[147],"each":[148],"case.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":5}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2019-06-07T00:00:00"}
