{"id":"https://openalex.org/W2027321980","doi":"https://doi.org/10.1109/cdc.2011.6161280","title":"A gradient method for geodesic data fitting on some symmetric Riemannian manifolds","display_name":"A gradient method for geodesic data fitting on some symmetric Riemannian manifolds","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2027321980","doi":"https://doi.org/10.1109/cdc.2011.6161280","mag":"2027321980"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6161280","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161280","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","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/A5059317241","display_name":"Quentin Rentmeesters","orcid":null},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Quentin Rentmeesters","raw_affiliation_strings":["Department of Mathematical Engineering, Universit\u00e9 catholique de Louvain, Louvain-la-Neuve, Belgium","Department of Mathematical Engineering, Universit\u00e9 catholique de Louvain, Avenue Georges Lemaitre 4, B-1348 Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering, Universit\u00e9 catholique de Louvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]},{"raw_affiliation_string":"Department of Mathematical Engineering, Universit\u00e9 catholique de Louvain, Avenue Georges Lemaitre 4, B-1348 Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5059317241"],"corresponding_institution_ids":["https://openalex.org/I95674353"],"apc_list":null,"apc_paid":null,"fwci":1.1455,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.76502909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"7141","last_page":"7146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9921000003814697,"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":0.9921000003814697,"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/T11325","display_name":"Inertial Sensor and Navigation","score":0.909600019454956,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/geodesic","display_name":"Geodesic","score":0.7489427328109741},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.7234103679656982},{"id":"https://openalex.org/keywords/tangent-bundle","display_name":"Tangent bundle","score":0.6360613107681274},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.5823569893836975},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.5460687875747681},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5168307423591614},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4780564606189728},{"id":"https://openalex.org/keywords/solving-the-geodesic-equations","display_name":"Solving the geodesic equations","score":0.46202075481414795},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.45903611183166504},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40084853768348694},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.377543568611145},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3576262593269348},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3551591634750366},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2843840420246124},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18890732526779175}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.7489427328109741},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.7234103679656982},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.6360613107681274},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.5823569893836975},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5460687875747681},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5168307423591614},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4780564606189728},{"id":"https://openalex.org/C161773026","wikidata":"https://www.wikidata.org/wiki/Q7559041","display_name":"Solving the geodesic equations","level":3,"score":0.46202075481414795},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.45903611183166504},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40084853768348694},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.377543568611145},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3576262593269348},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3551591634750366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2843840420246124},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18890732526779175},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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":2,"locations":[{"id":"doi:10.1109/cdc.2011.6161280","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161280","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:dial.uclouvain.be:boreal:109182","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/109182","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W205801760","https://openalex.org/W1509364003","https://openalex.org/W1572143211","https://openalex.org/W1804110266","https://openalex.org/W1912096629","https://openalex.org/W1947363732","https://openalex.org/W1982729005","https://openalex.org/W2029696139","https://openalex.org/W2036793545","https://openalex.org/W2045512849","https://openalex.org/W2089465567","https://openalex.org/W2109409043","https://openalex.org/W2120233471","https://openalex.org/W2125691646","https://openalex.org/W2128587390","https://openalex.org/W2159713859","https://openalex.org/W2573028792","https://openalex.org/W3038420293","https://openalex.org/W3047769892","https://openalex.org/W4205293427","https://openalex.org/W4206033904","https://openalex.org/W4206374124","https://openalex.org/W6673096895"],"related_works":["https://openalex.org/W2050728860","https://openalex.org/W4377864461","https://openalex.org/W2096403660","https://openalex.org/W2735816623","https://openalex.org/W4302293253","https://openalex.org/W4225110265","https://openalex.org/W2400724917","https://openalex.org/W2188104310","https://openalex.org/W4288322516","https://openalex.org/W2921497019"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,12,19,29],"method":[4,25],"to":[5,18,60],"compute":[6,61],"the":[7,34,38,43,48,76,83,98,104],"best":[8],"geodesic":[9],"approximation":[10],"of":[11,14,37,50,85],"set":[13,84],"points":[15],"that":[16],"belong":[17],"Riemannian":[20],"manifold":[21,106],"is":[22,26,45,58,68],"proposed.":[23],"This":[24],"based":[27],"on":[28,33,70],"gradient":[30,44],"descent":[31],"technique":[32,57],"tangent":[35],"bundle":[36],"manifold.":[39],"An":[40],"expression":[41],"for":[42],"derived":[46],"using":[47],"theory":[49],"Jacobi":[51,63],"fields":[52],"and":[53,75,103],"an":[54],"efficient":[55],"numerical":[56],"proposed":[59],"these":[62],"fields.":[64],"The":[65],"presented":[66],"approach":[67],"valid":[69],"any":[71],"locally":[72],"symmetric":[73,86],"space,":[74],"sphere":[77],"S":[78],"<sup":[79,94],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[80,92,95],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[81],",":[82,97],"positive":[87],"definite":[88],"matrices":[89],"P":[90],"<sub":[91],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[93],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">+</sup>":[96],"special":[99],"orthogonal":[100],"group":[101],"SO(3)":[102],"Grassmann":[105],"Grass(n;":[107],"p)":[108],"are":[109],"considered.":[110]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}