{"id":"https://openalex.org/W2096484739","doi":"https://doi.org/10.1109/cvpr.2008.4587422","title":"Clustering and dimensionality reduction on Riemannian manifolds","display_name":"Clustering and dimensionality reduction on Riemannian manifolds","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2096484739","doi":"https://doi.org/10.1109/cvpr.2008.4587422","mag":"2096484739"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2008.4587422","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2008.4587422","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE Conference on Computer Vision and Pattern Recognition","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/A5103357258","display_name":"Alvina Goh","orcid":null},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alvina Goh","raw_affiliation_strings":["Center for Imaging Science, Johns Hopkins University, Baltimore, MD, USA","Center for Imaging Sci., Johns Hopkins Univ., Baltimore, MD"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Imaging Science, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"Center for Imaging Sci., Johns Hopkins Univ., Baltimore, MD","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011256828","display_name":"Ren\u00e9 Vidal","orcid":"https://orcid.org/0000-0003-1838-0761"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rene Vidal","raw_affiliation_strings":["Center for Imaging Science, Johns Hopkins University, Baltimore, MD, USA","Center for Imaging Sci., Johns Hopkins Univ., Baltimore, MD"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Imaging Science, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"Center for Imaging Sci., Johns Hopkins Univ., Baltimore, MD","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1343,"has_fulltext":false,"cited_by_count":125,"citation_normalized_percentile":{"value":0.93592881,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9966999888420105,"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":0.9753999710083008,"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/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6269861459732056},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5870135426521301},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.5605099201202393},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.543587863445282},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.5239351391792297},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.44808071851730347},{"id":"https://openalex.org/keywords/pseudo-riemannian-manifold","display_name":"Pseudo-Riemannian manifold","score":0.43820920586586},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.43765896558761597},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4267132580280304},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.41734522581100464},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.39779767394065857},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3918517529964447},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18920430541038513},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.14336317777633667},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07987910509109497}],"concepts":[{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6269861459732056},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5870135426521301},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5605099201202393},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.543587863445282},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.5239351391792297},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.44808071851730347},{"id":"https://openalex.org/C121705324","wikidata":"https://www.wikidata.org/wiki/Q1510587","display_name":"Pseudo-Riemannian manifold","level":4,"score":0.43820920586586},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.43765896558761597},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4267132580280304},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.41734522581100464},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.39779767394065857},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3918517529964447},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18920430541038513},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.14336317777633667},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07987910509109497},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cvpr.2008.4587422","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2008.4587422","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W56210758","https://openalex.org/W1504242651","https://openalex.org/W1983496390","https://openalex.org/W2001141328","https://openalex.org/W2048192550","https://openalex.org/W2059640215","https://openalex.org/W2100078691","https://openalex.org/W2107018568","https://openalex.org/W2114190460","https://openalex.org/W2115992839","https://openalex.org/W2122108494","https://openalex.org/W2146610201","https://openalex.org/W2150903798","https://openalex.org/W2156718197","https://openalex.org/W2156838815","https://openalex.org/W2168108268","https://openalex.org/W2177347332","https://openalex.org/W2295046650","https://openalex.org/W2799061466","https://openalex.org/W3129186208","https://openalex.org/W4206033904","https://openalex.org/W4244494905","https://openalex.org/W4285719527","https://openalex.org/W6674845286","https://openalex.org/W6675860328","https://openalex.org/W6682755970"],"related_works":["https://openalex.org/W2999284236","https://openalex.org/W4362679437","https://openalex.org/W3104588897","https://openalex.org/W4297731962","https://openalex.org/W2125003829","https://openalex.org/W4300760355","https://openalex.org/W2611114005","https://openalex.org/W1531189931","https://openalex.org/W2031609484","https://openalex.org/W1989829336"],"abstract_inverted_index":{"We":[0,94],"propose":[1],"a":[2,13,19,68],"novel":[3],"algorithm":[4],"for":[5],"clustering":[6],"data":[7,23,54],"sampled":[8],"from":[9,32,56,71],"multiple":[10],"submanifolds":[11],"of":[12,21,26,42,67,78],"Riemannian":[14,35,44,48],"manifold.":[15],"First,":[16],"we":[17,61],"learn":[18],"representation":[20,74],"the":[22,43,53,64,72,76,79],"using":[24],"generalizations":[25,38],"local":[27,73],"nonlinear":[28],"dimensionality":[29],"reduction":[30],"algorithms":[31],"Euclidean":[33],"to":[34],"spaces.":[36],"Such":[37],"exploit":[39],"geometric":[40],"properties":[41],"space,":[45],"particularly":[46],"its":[47],"metric.":[49],"Then,":[50],"assuming":[51],"that":[52,63],"points":[55],"different":[57],"groups":[58],"are":[59],"separated,":[60],"show":[62],"null":[65],"space":[66],"matrix":[69],"built":[70],"gives":[75],"segmentation":[77,89,100],"data.":[80],"Our":[81],"method":[82],"is":[83],"computationally":[84],"simple":[85],"and":[86,101],"performs":[87],"automatic":[88],"without":[90],"requiring":[91],"user":[92],"initialization.":[93],"present":[95],"results":[96],"on":[97],"2-D":[98],"motion":[99],"diffusion":[102],"tensor":[103],"imaging":[104],"segmentation.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
