{"id":"https://openalex.org/W265981818","doi":"https://doi.org/10.4018/ijncr.2015040103","title":"Composition of Local Normal Coordinates and Polyhedral Geometry in Riemannian Manifold Learning","display_name":"Composition of Local Normal Coordinates and Polyhedral Geometry in Riemannian Manifold Learning","publication_year":2015,"publication_date":"2015-04-01","ids":{"openalex":"https://openalex.org/W265981818","doi":"https://doi.org/10.4018/ijncr.2015040103","mag":"265981818"},"language":"en","primary_location":{"id":"doi:10.4018/ijncr.2015040103","is_oa":false,"landing_page_url":"https://doi.org/10.4018/ijncr.2015040103","pdf_url":null,"source":{"id":"https://openalex.org/S1001844925","display_name":"International Journal of Natural Computing Research","issn_l":"1947-928X","issn":["1947-928X","1947-9298"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320424","host_organization_name":"IGI Global","host_organization_lineage":["https://openalex.org/P4310320424"],"host_organization_lineage_names":["IGI Global"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Natural Computing Research","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/A5076757263","display_name":"Gast\u00e3o Flor\u00eancio Miranda","orcid":"https://orcid.org/0000-0002-0967-6141"},"institutions":[{"id":"https://openalex.org/I190085865","display_name":"Universidade Federal de Sergipe","ror":"https://ror.org/028ka0n85","country_code":"BR","type":"education","lineage":["https://openalex.org/I190085865"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Gast\u00e3o F. Miranda Jr.","raw_affiliation_strings":["Department of Mathematics, Federal University of Sergipe, Sao Cristovao, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Federal University of Sergipe, Sao Cristovao, Brazil","institution_ids":["https://openalex.org/I190085865"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008848139","display_name":"Gilson A. Giraldi","orcid":"https://orcid.org/0000-0003-0623-9461"},"institutions":[{"id":"https://openalex.org/I4210142352","display_name":"Laborat\u00f3rio Nacional de Computa\u00e7\u00e3o Cient\u00edfica","ror":"https://ror.org/0498ekt05","country_code":"BR","type":"government","lineage":["https://openalex.org/I4210142352"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Gilson Giraldi","raw_affiliation_strings":["National Laboratory for Scientific Computing, Petropolis, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Laboratory for Scientific Computing, Petropolis, Brazil","institution_ids":["https://openalex.org/I4210142352"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075626456","display_name":"Carlos Eduardo Thomaz","orcid":"https://orcid.org/0000-0001-5566-1963"},"institutions":[{"id":"https://openalex.org/I139221136","display_name":"Centro Universit\u00e1rio FEI","ror":"https://ror.org/007kf5222","country_code":"BR","type":"education","lineage":["https://openalex.org/I139221136"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Carlos E. Thomaz","raw_affiliation_strings":["Department of Electrical Engineering, University Center of FEI, Sao Bernardo do Campo, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University Center of FEI, Sao Bernardo do Campo, Brazil","institution_ids":["https://openalex.org/I139221136"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091821614","display_name":"Daniel Mill\u00e1n","orcid":"https://orcid.org/0000-0001-6917-0460"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Daniel Mill\u00e0n","raw_affiliation_strings":["Polytechnic University of Catalonia-Barcelona, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Polytechnic University of Catalonia-Barcelona, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5616,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72973682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"5","issue":"2","first_page":"37","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9901000261306763,"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/T10057","display_name":"Face and Expression Recognition","score":0.9901000261306763,"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/T10320","display_name":"Neural Networks and Applications","score":0.9896000027656555,"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/T10535","display_name":"Landslides and related hazards","score":0.9851999878883362,"subfield":{"id":"https://openalex.org/subfields/2308","display_name":"Management, Monitoring, Policy and Law"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.658840537071228},{"id":"https://openalex.org/keywords/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.6570324897766113},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.6527541279792786},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.6145449280738831},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.5964120030403137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5682517886161804},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5286275148391724},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.5103973746299744},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5023519992828369},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.4886482357978821},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.47111156582832336},{"id":"https://openalex.org/keywords/coordinate-system","display_name":"Coordinate system","score":0.4343082904815674},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4299704134464264},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4210721552371979},{"id":"https://openalex.org/keywords/pseudo-riemannian-manifold","display_name":"Pseudo-Riemannian manifold","score":0.41925016045570374},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.41868090629577637},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4177525043487549},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.41621237993240356},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22489190101623535},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20300579071044922},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.12732312083244324},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0938866138458252},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.08274051547050476}],"concepts":[{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.658840537071228},{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.6570324897766113},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.6527541279792786},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.6145449280738831},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.5964120030403137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5682517886161804},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5286275148391724},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.5103973746299744},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5023519992828369},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.4886482357978821},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.47111156582832336},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.4343082904815674},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4299704134464264},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4210721552371979},{"id":"https://openalex.org/C121705324","wikidata":"https://www.wikidata.org/wiki/Q1510587","display_name":"Pseudo-Riemannian manifold","level":4,"score":0.41925016045570374},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.41868090629577637},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4177525043487549},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.41621237993240356},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22489190101623535},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20300579071044922},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.12732312083244324},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0938866138458252},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.08274051547050476},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"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":2,"locations":[{"id":"doi:10.4018/ijncr.2015040103","is_oa":false,"landing_page_url":"https://doi.org/10.4018/ijncr.2015040103","pdf_url":null,"source":{"id":"https://openalex.org/S1001844925","display_name":"International Journal of Natural Computing Research","issn_l":"1947-928X","issn":["1947-928X","1947-9298"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320424","host_organization_name":"IGI Global","host_organization_lineage":["https://openalex.org/P4310320424"],"host_organization_lineage_names":["IGI Global"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Natural Computing Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:igg:jncr00:v:5:y:2015:i:2:p:37-68","is_oa":false,"landing_page_url":"http://services.igi-global.com/resolvedoi/resolve.aspx?doi=10.4018/ijncr.2015040103","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5799999833106995,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W254308459","https://openalex.org/W434012021","https://openalex.org/W1480376833","https://openalex.org/W1742512077","https://openalex.org/W1965534165","https://openalex.org/W1971171352","https://openalex.org/W2001141328","https://openalex.org/W2010441082","https://openalex.org/W2041657594","https://openalex.org/W2053186076","https://openalex.org/W2063385051","https://openalex.org/W2071569218","https://openalex.org/W2097308346","https://openalex.org/W2101234009","https://openalex.org/W2116931174","https://openalex.org/W2125003829","https://openalex.org/W2140095548","https://openalex.org/W2157576781","https://openalex.org/W2186590998","https://openalex.org/W2294536272","https://openalex.org/W3023608713","https://openalex.org/W4252316495","https://openalex.org/W4298238668"],"related_works":["https://openalex.org/W2546668543","https://openalex.org/W334503494","https://openalex.org/W4300760355","https://openalex.org/W2155379735","https://openalex.org/W2949438187","https://openalex.org/W4291625303","https://openalex.org/W2059474323","https://openalex.org/W2737579912","https://openalex.org/W1532125927","https://openalex.org/W1975282624"],"abstract_inverted_index":{"The":[0],"Local":[1],"Riemannian":[2,37],"Manifold":[3],"Learning":[4],"(LRML)":[5],"recovers":[6],"the":[7,21,32,36,43,48,52,65,73,86,92,106,124,133,140,143,146,149,153],"manifold":[8,38,44],"topology":[9],"and":[10,136,155,163],"geometry":[11,121,157],"behind":[12],"database":[13],"samples":[14],"through":[15],"normal":[16,107],"coordinate":[17,108],"neighborhoods":[18,109],"computed":[19],"by":[20,99],"exponential":[22],"map.":[23],"Besides,":[24,64],"LRML":[25,87,98,125,150],"uses":[26],"barycentric":[27],"coordinates":[28],"to":[29,35,41,77,104,123,127],"go":[30],"from":[31],"parameter":[33],"space":[34,61],"in":[39,85],"order":[40],"perform":[42],"synthesis.":[45],"Despite":[46],"of":[47,50,72,97,148],"advantages":[49],"LRML,":[51],"obtained":[53],"parameterization":[54],"cannot":[55],"be":[56,78],"used":[57],"as":[58],"a":[59,69,101,112,119],"representational":[60,114],"without":[62],"ambiguities.":[63],"synthesis":[66,134,162],"process":[67,135],"needs":[68],"simplicial":[70],"decomposition":[71],"lower":[74],"dimensional":[75],"domain":[76],"efficiently":[79],"performed,":[80],"which":[81],"is":[82],"not":[83],"considered":[84],"proposal.":[88],"In":[89,139],"this":[90],"paper,":[91],"authors":[93,144],"address":[94],"these":[95],"drawbacks":[96],"using":[100],"composition":[102,154],"procedure":[103],"combine":[105],"for":[110,132,159],"building":[111],"suitable":[113],"space.":[115],"Moreover,":[116],"they":[117],"incorporate":[118],"polyhedral":[120],"framework":[122],"method":[126],"give":[128],"an":[129],"efficient":[130],"background":[131],"data":[137,164],"analysis.":[138],"computational":[141],"experiments,":[142],"verify":[145],"efficiency":[147],"combined":[151],"with":[152],"discrete":[156],"frameworks":[158],"dimensionality":[160],"reduction,":[161],"exploration.":[165]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}