{"id":"https://openalex.org/W2588283913","doi":"https://doi.org/10.1109/cisp-bmei.2016.7853029","title":"A flow based approach for learning multiple manifolds","display_name":"A flow based approach for learning multiple manifolds","publication_year":2016,"publication_date":"2016-10-01","ids":{"openalex":"https://openalex.org/W2588283913","doi":"https://doi.org/10.1109/cisp-bmei.2016.7853029","mag":"2588283913"},"language":"en","primary_location":{"id":"doi:10.1109/cisp-bmei.2016.7853029","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cisp-bmei.2016.7853029","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 9th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI)","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/A5101743038","display_name":"Gang Shen","orcid":"https://orcid.org/0000-0001-5961-8110"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Gang Shen","raw_affiliation_strings":["School of Software Engineering, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"School of Software Engineering, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101431817","display_name":"Dan Han","orcid":"https://orcid.org/0000-0002-9578-0243"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dan Han","raw_affiliation_strings":["School of Software Engineering, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"School of Software Engineering, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101743038"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":0.4285,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.80825654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":null,"first_page":"1905","last_page":"1910"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9864000082015991,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9864000082015991,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9864000082015991,"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/T12417","display_name":"Morphological variations and asymmetry","score":0.9746999740600586,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.7720165848731995},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.6909627914428711},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.6600223779678345},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5724126100540161},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5684384703636169},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.536713182926178},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4795779585838318},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47940632700920105},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4720913767814636},{"id":"https://openalex.org/keywords/manifold-alignment","display_name":"Manifold alignment","score":0.4716733396053314},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.45901715755462646},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4034052789211273},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3843090534210205},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3754197657108307},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3620922565460205},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34987151622772217},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1685466766357422},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14549779891967773},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.11849924921989441},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.10230386257171631},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07266193628311157}],"concepts":[{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.7720165848731995},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.6909627914428711},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.6600223779678345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5724126100540161},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5684384703636169},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.536713182926178},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4795779585838318},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47940632700920105},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4720913767814636},{"id":"https://openalex.org/C153120616","wikidata":"https://www.wikidata.org/wiki/Q17068315","display_name":"Manifold alignment","level":4,"score":0.4716733396053314},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.45901715755462646},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4034052789211273},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3843090534210205},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3754197657108307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3620922565460205},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34987151622772217},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1685466766357422},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14549779891967773},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.11849924921989441},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.10230386257171631},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07266193628311157},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cisp-bmei.2016.7853029","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cisp-bmei.2016.7853029","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 9th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6700000166893005,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1518600725","https://openalex.org/W1540288699","https://openalex.org/W1981826826","https://openalex.org/W1997388358","https://openalex.org/W2000631868","https://openalex.org/W2025064394","https://openalex.org/W2107018255","https://openalex.org/W2128330514","https://openalex.org/W2129812935","https://openalex.org/W2144767994","https://openalex.org/W2145094598","https://openalex.org/W2157063016","https://openalex.org/W2163922914","https://openalex.org/W2295046650","https://openalex.org/W2315519281","https://openalex.org/W2997574889","https://openalex.org/W3104353475","https://openalex.org/W6681096077","https://openalex.org/W6682872970","https://openalex.org/W6699317558"],"related_works":["https://openalex.org/W2387045723","https://openalex.org/W117517268","https://openalex.org/W2397338926","https://openalex.org/W2085003924","https://openalex.org/W2573981081","https://openalex.org/W2384392227","https://openalex.org/W2380477800","https://openalex.org/W1976359930","https://openalex.org/W2119945967","https://openalex.org/W2888431323"],"abstract_inverted_index":{"In":[0],"this":[1,43],"paper,":[2],"we":[3],"investigate":[4],"the":[5,49,64,96,108,117,120],"problem":[6],"of":[7,56,66,69,92,119],"learning":[8,47],"multiple":[9],"overlapped":[10],"manifolds":[11,21,57],"from":[12],"data":[13,35],"samples":[14],"with":[15],"noise.":[16],"Learning":[17],"low":[18],"dimensional":[19,25],"nonlinear":[20],"embedded":[22],"in":[23,33,42,71,113],"high":[24],"Euclidean":[26],"space":[27],"has":[28],"been":[29],"an":[30,53,89],"important":[31],"issue":[32],"many":[34],"driven":[36],"pattern":[37],"analysis":[38],"applications.":[39],"The":[40,60],"work":[41],"paper":[44],"extends":[45],"manifold":[46,80,110],"into":[48],"complex":[50],"situations":[51],"where":[52],"unknown":[54],"number":[55],"may":[58],"overlap.":[59],"approach":[61],"proposed":[62,121],"introduces":[63],"notion":[65],"flow":[67,87],"consisting":[68],"multi-agents":[70],"a":[72,75,79],"formation":[73],"exploring":[74],"smooth":[76],"curve":[77],"on":[78],"and":[81,98],"thus":[82],"separating":[83],"different":[84],"manifolds.":[85],"A":[86],"generates":[88],"ordered":[90],"sequence":[91],"neighborhoods":[93],"visited":[94],"by":[95],"agents":[97],"can":[99],"be":[100],"used":[101],"to":[102,106],"simplify":[103],"elastic":[104],"mapping":[105],"discover":[107],"principal":[109],"structures.":[111],"Simulations":[112],"various":[114],"settings":[115],"demonstrate":[116],"effectiveness":[118],"approach.":[122]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}