{"id":"https://openalex.org/W1604571752","doi":"https://doi.org/10.1007/978-3-642-13278-0_24","title":"A Closed-Form Solution to the Problem of Averaging over the Lie Group of Special Orthogonal Matrices","display_name":"A Closed-Form Solution to the Problem of Averaging over the Lie Group of Special Orthogonal Matrices","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1604571752","doi":"https://doi.org/10.1007/978-3-642-13278-0_24","mag":"1604571752"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-13278-0_24","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-13278-0_24","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5079056700","display_name":"Simone Fiori","orcid":"https://orcid.org/0000-0001-5964-7464"},"institutions":[{"id":"https://openalex.org/I122534668","display_name":"Marche Polytechnic University","ror":"https://ror.org/00x69rs40","country_code":"IT","type":"education","lineage":["https://openalex.org/I122534668"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Simone Fiori","raw_affiliation_strings":["Dipartimento di Ingegneria Biomedica, Elettronica e Telecomunicazioni (DiBET), Universit\u00e0 Politecnica delle Marche, Ancona, Italy","[Dipartimento di Ingegneria Biomedica, Elettronica e Telecomunicazioni (DiBET), Universit\u00e0 Politecnica delle Marche, Ancona, Italy]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria Biomedica, Elettronica e Telecomunicazioni (DiBET), Universit\u00e0 Politecnica delle Marche, Ancona, Italy","institution_ids":["https://openalex.org/I122534668"]},{"raw_affiliation_string":"[Dipartimento di Ingegneria Biomedica, Elettronica e Telecomunicazioni (DiBET), Universit\u00e0 Politecnica delle Marche, Ancona, Italy]","institution_ids":["https://openalex.org/I122534668"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079056700"],"corresponding_institution_ids":["https://openalex.org/I122534668"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.19218652,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"185","last_page":"192"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9984999895095825,"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/T10320","display_name":"Neural Networks and Applications","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.5791361331939697},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.5783453583717346},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5642682313919067},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.525990903377533},{"id":"https://openalex.org/keywords/orthogonal-group","display_name":"Orthogonal group","score":0.494354248046875},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4744316637516022},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.444835364818573},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4313940107822418},{"id":"https://openalex.org/keywords/closed-form-expression","display_name":"Closed-form expression","score":0.4245883524417877},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.412636935710907},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3990502953529358},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.363777756690979},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32628318667411804},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29768624901771545},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16512557864189148},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.11570215225219727},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05506390333175659}],"concepts":[{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.5791361331939697},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.5783453583717346},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5642682313919067},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.525990903377533},{"id":"https://openalex.org/C146561895","wikidata":"https://www.wikidata.org/wiki/Q1783179","display_name":"Orthogonal group","level":2,"score":0.494354248046875},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4744316637516022},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.444835364818573},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4313940107822418},{"id":"https://openalex.org/C4530962","wikidata":"https://www.wikidata.org/wiki/Q777407","display_name":"Closed-form expression","level":2,"score":0.4245883524417877},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.412636935710907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3990502953529358},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.363777756690979},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32628318667411804},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29768624901771545},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16512557864189148},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.11570215225219727},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05506390333175659},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-642-13278-0_24","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-13278-0_24","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:iris.univpm.it:11566/73859","is_oa":false,"landing_page_url":"http://hdl.handle.net/11566/73859","pdf_url":null,"source":{"id":"https://openalex.org/S4306402571","display_name":"Universit\u00e0 Politecnica delle Marche (Universit\u00e0 Politecnica delle Marche)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122534668","host_organization_name":"Marche Polytechnic University","host_organization_lineage":["https://openalex.org/I122534668"],"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":"info:eu-repo/semantics/bookPart"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1490535540","https://openalex.org/W1587069887","https://openalex.org/W2017587562","https://openalex.org/W2100687344","https://openalex.org/W2125139728","https://openalex.org/W2155813218","https://openalex.org/W2164430105","https://openalex.org/W2169019105","https://openalex.org/W2169736182","https://openalex.org/W2496326252","https://openalex.org/W2595840341","https://openalex.org/W2610184409","https://openalex.org/W2978329087","https://openalex.org/W4236654676"],"related_works":["https://openalex.org/W1638580935","https://openalex.org/W2625783959","https://openalex.org/W1993807234","https://openalex.org/W4299808573","https://openalex.org/W2394160247","https://openalex.org/W2963067926","https://openalex.org/W1998410259","https://openalex.org/W2763193512","https://openalex.org/W2899071019","https://openalex.org/W1604571752"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-10T14:10:52.464848","created_date":"2025-10-10T00:00:00"}