{"id":"https://openalex.org/W2139998576","doi":"https://doi.org/10.1109/tsmca.2002.1021114","title":"Approximation of n-dimensional data using spherical and ellipsoidal primitives","display_name":"Approximation of n-dimensional data using spherical and ellipsoidal primitives","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W2139998576","doi":"https://doi.org/10.1109/tsmca.2002.1021114","mag":"2139998576"},"language":"en","primary_location":{"id":"doi:10.1109/tsmca.2002.1021114","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmca.2002.1021114","pdf_url":null,"source":{"id":"https://openalex.org/S4210201610","display_name":"IEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans","issn_l":"1083-4427","issn":["1083-4427","1558-2426"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans","raw_type":"journal-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/A5041746196","display_name":"Giuseppe C. Calafiore","orcid":"https://orcid.org/0000-0002-6428-5653"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Polytechnic University of Turin","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"G. Calafiore","raw_affiliation_strings":["Dipartimento di Automatica de Informatica, Politecnico di Torino, Torino, Italy","Dipt. di Automatica e Informatica, Politecnico di Torino, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Automatica de Informatica, Politecnico di Torino, Torino, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Dipt. di Automatica e Informatica, Politecnico di Torino, Italy","institution_ids":["https://openalex.org/I177477856"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041746196"],"corresponding_institution_ids":["https://openalex.org/I177477856"],"apc_list":null,"apc_paid":null,"fwci":0.6976,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.71867807,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"32","issue":"2","first_page":"269","last_page":"278"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12549","display_name":"Image and Object Detection Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12549","display_name":"Image and Object Detection Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9929999709129333,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ellipsoid","display_name":"Ellipsoid","score":0.8984383344650269},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.641796886920929},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.6294130086898804},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5531554818153381},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.5517063140869141},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5394538044929504},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.498183012008667},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.48154857754707336},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.47310781478881836},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4205433428287506},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41900381445884705},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3256877064704895},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2842540144920349},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2778518795967102},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0899103581905365}],"concepts":[{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.8984383344650269},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.641796886920929},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.6294130086898804},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5531554818153381},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.5517063140869141},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5394538044929504},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.498183012008667},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.48154857754707336},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.47310781478881836},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4205433428287506},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41900381445884705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3256877064704895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2842540144920349},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2778518795967102},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0899103581905365},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsmca.2002.1021114","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmca.2002.1021114","pdf_url":null,"source":{"id":"https://openalex.org/S4210201610","display_name":"IEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans","issn_l":"1083-4427","issn":["1083-4427","1558-2426"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.421.1322","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.421.1322","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://staff.polito.it/giuseppe.calafiore/Documenti/Papers/Ellipsoidal Approximation_TSMC-02.pdf","raw_type":"text"},{"id":"pmh:oai:porto.polito.it:1398195","is_oa":false,"landing_page_url":"http://porto.polito.it/1398195/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1083-4427","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6399999856948853,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1509069826","https://openalex.org/W1555614281","https://openalex.org/W1632601927","https://openalex.org/W1963753244","https://openalex.org/W1981609785","https://openalex.org/W1991923460","https://openalex.org/W2000134108","https://openalex.org/W2009086487","https://openalex.org/W2024318675","https://openalex.org/W2045181334","https://openalex.org/W2053197265","https://openalex.org/W2055356142","https://openalex.org/W2100440346","https://openalex.org/W2102677843","https://openalex.org/W2105235982","https://openalex.org/W2108517239","https://openalex.org/W2112479957","https://openalex.org/W2113003378","https://openalex.org/W2119947613","https://openalex.org/W2129249398","https://openalex.org/W2140427427","https://openalex.org/W2149659501","https://openalex.org/W2151984205","https://openalex.org/W2153178980","https://openalex.org/W2153361852","https://openalex.org/W2489822048","https://openalex.org/W2495457432","https://openalex.org/W2498631646","https://openalex.org/W2912522929","https://openalex.org/W3210839039","https://openalex.org/W6656415848","https://openalex.org/W6677777478"],"related_works":["https://openalex.org/W1970960579","https://openalex.org/W2408196627","https://openalex.org/W4300721055","https://openalex.org/W2402215390","https://openalex.org/W2035532675","https://openalex.org/W2028140316","https://openalex.org/W4290773469","https://openalex.org/W4297581286","https://openalex.org/W2131728408","https://openalex.org/W2952368903"],"abstract_inverted_index":{"This":[0],"paper":[1,47],"discusses":[2],"the":[3,34,46,60,73],"problem":[4,36],"of":[5,41,56,85],"approximating":[6],"data":[7],"points":[8],"in":[9,39,54],"n-dimensional":[10],"Euclidean":[11],"space":[12],"using":[13],"spherical":[14,25],"and":[15,58,88],"ellipsoidal":[16,35,83],"surfaces.":[17],"A":[18,66],"closed":[19],"form":[20],"solution":[21,32],"is":[22,37,69],"provided":[23],"for":[24,33,51],"approximation,":[26],"while":[27],"an":[28],"efficient,":[29],"globally":[30],"optimal":[31],"proposed":[38],"terms":[40],"semidefinite":[42],"programming.":[43],"In":[44],"addition,":[45],"presents":[48],"a":[49],"result":[50],"robust":[52],"fitting":[53],"presence":[55],"outliers,":[57],"illustrates":[59],"theory":[61],"with":[62],"several":[63],"numerical":[64],"examples.":[65],"brief":[67],"survey":[68],"also":[70],"presented":[71],"on":[72],"solutions":[74],"to":[75],"other":[76],"relevant":[77],"geometric":[78],"approximation":[79],"problems,":[80],"such":[81],"as":[82],"covering":[84],"convex":[86],"hulls":[87],"pattern":[89],"separation.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}