{"id":"https://openalex.org/W4220664058","doi":"https://doi.org/10.3390/a15030092","title":"Mean Estimation on the Diagonal of Product Manifolds","display_name":"Mean Estimation on the Diagonal of Product Manifolds","publication_year":2022,"publication_date":"2022-03-10","ids":{"openalex":"https://openalex.org/W4220664058","doi":"https://doi.org/10.3390/a15030092"},"language":"en","primary_location":{"id":"doi:10.3390/a15030092","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15030092","pdf_url":"https://www.mdpi.com/1999-4893/15/3/92/pdf?version=1646909023","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/15/3/92/pdf?version=1646909023","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015550888","display_name":"Mathias H\u00f8jgaard Jensen","orcid":"https://orcid.org/0000-0002-0320-7897"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Mathias H\u00f8jgaard Jensen","raw_affiliation_strings":["Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103194945","display_name":"Stefan Sommer","orcid":"https://orcid.org/0000-0001-6784-0328"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Stefan Sommer","raw_affiliation_strings":["Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103194945"],"corresponding_institution_ids":["https://openalex.org/I124055696"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.8037,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67133015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"3","first_page":"92","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9796000123023987,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9449999928474426,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.7364548444747925},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5829501748085022},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5783532857894897},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5325846672058105},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5303866267204285},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5048002004623413},{"id":"https://openalex.org/keywords/sample-mean-and-sample-covariance","display_name":"Sample mean and sample covariance","score":0.45361095666885376},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44466909766197205},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.43323129415512085},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4265870451927185},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.41174086928367615},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36679771542549133},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23329177498817444},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14834502339363098},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1100379228591919}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.7364548444747925},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5829501748085022},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5783532857894897},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5325846672058105},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5303866267204285},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5048002004623413},{"id":"https://openalex.org/C181243257","wikidata":"https://www.wikidata.org/wiki/Q1693522","display_name":"Sample mean and sample covariance","level":3,"score":0.45361095666885376},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44466909766197205},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.43323129415512085},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4265870451927185},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.41174086928367615},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36679771542549133},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23329177498817444},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14834502339363098},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1100379228591919},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/a15030092","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15030092","pdf_url":"https://www.mdpi.com/1999-4893/15/3/92/pdf?version=1646909023","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/cd8487d5-749c-41e4-a429-65f567a5749f","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/cd8487d5-749c-41e4-a429-65f567a5749f","pdf_url":"https://curis.ku.dk/ws/files/301143048/Mean_Estimation_on_the_Diagonal_of_Product_Manifolds.pdf","source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Jensen , M H & Sommer , S 2022 , ' Mean Estimation on the Diagonal of Product Manifolds ' , Algorithms , vol. 15 , no. 3 , 92 , pp. 1-16 . https://doi.org/10.3390/a15030092","raw_type":"article"},{"id":"pmh:oai:doaj.org/article:b61d050e387b42acadf5f33ca65cf07d","is_oa":true,"landing_page_url":"https://doaj.org/article/b61d050e387b42acadf5f33ca65cf07d","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 15, Iss 3, p 92 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/15/3/92/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a15030092","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 15; Issue 3; Pages: 92","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a15030092","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15030092","pdf_url":"https://www.mdpi.com/1999-4893/15/3/92/pdf?version=1646909023","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1519125637","display_name":null,"funder_award_id":"22924","funder_id":"https://openalex.org/F4320310490","funder_display_name":"Villum Fonden"},{"id":"https://openalex.org/G1860862902","display_name":null,"funder_award_id":"00022924","funder_id":"https://openalex.org/F4320310489","funder_display_name":"Velux Fonden"},{"id":"https://openalex.org/G7119644066","display_name":null,"funder_award_id":"40582","funder_id":"https://openalex.org/F4320310490","funder_display_name":"Villum Fonden"},{"id":"https://openalex.org/G783019258","display_name":null,"funder_award_id":"NNF18OC0052000","funder_id":"https://openalex.org/F4320325957","funder_display_name":"Novo Nordisk Fonden"},{"id":"https://openalex.org/G7991563841","display_name":null,"funder_award_id":"NNF18OC0052000","funder_id":"https://openalex.org/F4320322436","funder_display_name":"Novo Nordisk"}],"funders":[{"id":"https://openalex.org/F4320310489","display_name":"Velux Fonden","ror":"https://ror.org/007ww2d15"},{"id":"https://openalex.org/F4320310490","display_name":"Villum Fonden","ror":"https://ror.org/007ww2d15"},{"id":"https://openalex.org/F4320322436","display_name":"Novo Nordisk","ror":"https://ror.org/0435rc536"},{"id":"https://openalex.org/F4320325957","display_name":"Novo Nordisk Fonden","ror":"https://ror.org/04txyc737"},{"id":"https://openalex.org/F4320337744","display_name":"Chemical Sciences, Geosciences, and Biosciences Division","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4220664058.pdf","grobid_xml":"https://content.openalex.org/works/W4220664058.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W21251301","https://openalex.org/W44521033","https://openalex.org/W1501943740","https://openalex.org/W1531413759","https://openalex.org/W1561367079","https://openalex.org/W1563333929","https://openalex.org/W1852328762","https://openalex.org/W1983496390","https://openalex.org/W2005669468","https://openalex.org/W2006302620","https://openalex.org/W2033321949","https://openalex.org/W2217701558","https://openalex.org/W2318756515","https://openalex.org/W2436131410","https://openalex.org/W2616907326","https://openalex.org/W2736563299","https://openalex.org/W2780557656","https://openalex.org/W2913975641","https://openalex.org/W2963176114","https://openalex.org/W2963480507","https://openalex.org/W2963746096","https://openalex.org/W2963772315","https://openalex.org/W2971398000","https://openalex.org/W3004021480","https://openalex.org/W3024254178","https://openalex.org/W3036550760","https://openalex.org/W3104146538","https://openalex.org/W3106318495","https://openalex.org/W3186860629","https://openalex.org/W3210503141","https://openalex.org/W4295632409","https://openalex.org/W6714750765"],"related_works":["https://openalex.org/W1978591761","https://openalex.org/W4287661821","https://openalex.org/W3133864228","https://openalex.org/W4353103777","https://openalex.org/W1977009394","https://openalex.org/W2951269968","https://openalex.org/W2946352054","https://openalex.org/W3127827089","https://openalex.org/W2546668543","https://openalex.org/W2952208990"],"abstract_inverted_index":{"Computing":[0],"sample":[1],"means":[2,155],"on":[3,156],"Riemannian":[4],"manifolds":[5],"is":[6,52],"typically":[7],"computationally":[8],"costly,":[9],"as":[10],"exemplified":[11],"by":[12,111],"computation":[13],"of":[14,31,148,153],"the":[15,79,86,90,122,130,134,146,149],"Fr\u00e9chet":[16,81],"mean,":[17],"which":[18],"often":[19],"requires":[20],"finding":[21],"minimizing":[22],"geodesics":[23,40],"to":[24,46,54,78,120],"each":[25,29],"data":[26],"point":[27],"for":[28,39,133],"step":[30],"an":[32,76],"iterative":[33],"optimization":[34,49],"scheme.":[35],"When":[36],"closed-form":[37],"expressions":[38],"are":[41],"not":[42,104],"available,":[43],"this":[44,110],"leads":[45],"a":[47,98,113,117,125],"nested":[48,106],"problem":[50],"that":[51,102],"costly":[53],"solve.":[55],"The":[56,71],"implied":[57],"computational":[58],"cost":[59],"impacts":[60],"applications":[61],"in":[62,67,116],"both":[63],"geometric":[64,68],"statistics":[65],"and":[66,89,143],"deep":[69],"learning.":[70],"weighted":[72,80,91],"diffusion":[73,87,92],"mean":[74,88,93,136],"offers":[75],"alternative":[77],"mean.":[82],"We":[83,108,128],"show":[84],"how":[85],"can":[94],"be":[95],"estimated":[96],"with":[97,151],"stochastic":[99],"simulation":[100,141],"scheme":[101],"does":[103],"require":[105],"optimization.":[107],"achieve":[109],"conditioning":[112],"Brownian":[114],"motion":[115],"product":[118],"manifold":[119],"hit":[121],"diagonal":[123],"at":[124],"predetermined":[126],"time.":[127],"develop":[129,139],"theoretical":[131],"foundation":[132],"sampling-based":[135],"estimation,":[137],"we":[138,144],"two":[140,157],"schemes,":[142],"demonstrate":[145],"applicability":[147],"method":[150],"examples":[152],"sampled":[154],"manifolds.":[158]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2022-04-03T00:00:00"}
