{"id":"https://openalex.org/W1990113521","doi":"https://doi.org/10.1109/grc.2013.6740451","title":"An error analysis on locally linear embedding","display_name":"An error analysis on locally linear embedding","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W1990113521","doi":"https://doi.org/10.1109/grc.2013.6740451","mag":"1990113521"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2013.6740451","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2013.6740451","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE International Conference on Granular Computing (GrC)","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/A5100364007","display_name":"Peng Zhang","orcid":"https://orcid.org/0000-0001-5198-882X"},"institutions":[{"id":"https://openalex.org/I4210115813","display_name":"China National Commission for Disaster Reduction","ror":"https://ror.org/029j8j127","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210115813"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peng Zhang","raw_affiliation_strings":["Data Center, National Disaster Reduction Center of China, Beijing, P.R. China","Data Center, Nat. Disaster Reduction Center of China, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Center, National Disaster Reduction Center of China, Beijing, P.R. China","institution_ids":["https://openalex.org/I4210115813"]},{"raw_affiliation_string":"Data Center, Nat. Disaster Reduction Center of China, Beijing, China","institution_ids":["https://openalex.org/I4210115813"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089785339","display_name":"Chunbo Fan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210115813","display_name":"China National Commission for Disaster Reduction","ror":"https://ror.org/029j8j127","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210115813"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunbo Fan","raw_affiliation_strings":["Data Center, National Disaster Reduction Center of China, Beijing, P.R. China","Data Center, Nat. Disaster Reduction Center of China, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Center, National Disaster Reduction Center of China, Beijing, P.R. China","institution_ids":["https://openalex.org/I4210115813"]},{"raw_affiliation_string":"Data Center, Nat. Disaster Reduction Center of China, Beijing, China","institution_ids":["https://openalex.org/I4210115813"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078825613","display_name":"Yuanyuan Ren","orcid":"https://orcid.org/0000-0001-7802-2128"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210134982","display_name":"Institute of Microbiology","ror":"https://ror.org/047yhep71","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210134982"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanyuan Ren","raw_affiliation_strings":["Institute of Microbiology, Chinese Academy of Sciences, Beijing, P.R. China","Inst. of Microbiol., Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Microbiology, Chinese Academy of Sciences, Beijing, P.R. China","institution_ids":["https://openalex.org/I4210134982","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Inst. of Microbiol., Beijing, China","institution_ids":["https://openalex.org/I4210134982"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024736241","display_name":"Zhou Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I4210115813","display_name":"China National Commission for Disaster Reduction","ror":"https://ror.org/029j8j127","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210115813"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou Sun","raw_affiliation_strings":["Data Center, National Disaster Reduction Center of China, Beijing, P.R. China","Data Center, Nat. Disaster Reduction Center of China, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Center, National Disaster Reduction Center of China, Beijing, P.R. China","institution_ids":["https://openalex.org/I4210115813"]},{"raw_affiliation_string":"Data Center, Nat. Disaster Reduction Center of China, Beijing, China","institution_ids":["https://openalex.org/I4210115813"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06546719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"102","issue":null,"first_page":"437","last_page":"442"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10205","display_name":"Advanced Fiber Optic Sensors","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10205","display_name":"Advanced Fiber Optic Sensors","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference techniques","score":0.979200005531311,"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/T11799","display_name":"Adhesion, Friction, and Surface Interactions","score":0.9692999720573425,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.9104793071746826},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.8060103058815002},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.7888312339782715},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7716884613037109},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.7262709140777588},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6245547533035278},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5806070566177368},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5661040544509888},{"id":"https://openalex.org/keywords/isomap","display_name":"Isomap","score":0.4980940818786621},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.46305251121520996},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42188021540641785},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.38904115557670593},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36311474442481995},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3618490993976593},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21643108129501343}],"concepts":[{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.9104793071746826},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.8060103058815002},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.7888312339782715},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7716884613037109},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.7262709140777588},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6245547533035278},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5806070566177368},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5661040544509888},{"id":"https://openalex.org/C2778626561","wikidata":"https://www.wikidata.org/wiki/Q6086067","display_name":"Isomap","level":4,"score":0.4980940818786621},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.46305251121520996},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42188021540641785},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.38904115557670593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36311474442481995},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3618490993976593},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21643108129501343},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.0},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/grc.2013.6740451","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2013.6740451","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE International Conference on Granular Computing (GrC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1578196132","https://openalex.org/W1679913846","https://openalex.org/W1966949944","https://openalex.org/W2001141328","https://openalex.org/W2006554089","https://openalex.org/W2011162472","https://openalex.org/W2027230374","https://openalex.org/W2034383054","https://openalex.org/W2044439250","https://openalex.org/W2047870719","https://openalex.org/W2053186076","https://openalex.org/W2063532964","https://openalex.org/W2077776048","https://openalex.org/W2097308346","https://openalex.org/W2125003829","https://openalex.org/W2156838815","https://openalex.org/W2610857016","https://openalex.org/W3013880646","https://openalex.org/W3038420293","https://openalex.org/W4206033904","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2375574759","https://openalex.org/W1489327846","https://openalex.org/W4287375746","https://openalex.org/W3124275785","https://openalex.org/W2037225398","https://openalex.org/W2132734978","https://openalex.org/W2166963679","https://openalex.org/W2364555648","https://openalex.org/W2352321395","https://openalex.org/W3193686696"],"abstract_inverted_index":{"Locally":[0],"linear":[1],"embedding":[2,90],"(LLE)":[3],"has":[4],"been":[5,41],"proved":[6],"to":[7,29,34,71,98],"an":[8,17,54],"efficient":[9],"tool":[10],"for":[11,47],"nonlinear":[12],"dimensionality":[13],"reduction.":[14],"It":[15],"is":[16,96],"unsupervised":[18],"learning":[19,45],"method":[20,60],"with":[21],"various":[22],"attractive":[23],"properties,":[24],"such":[25],"as":[26],"few":[27,38],"parameters":[28],"select":[30],"and":[31,61,91],"non":[32],"prone":[33],"local":[35,86],"minima.":[36],"However,":[37],"works":[39],"have":[40],"done":[42],"on":[43,57],"analyzing":[44],"errors":[46,83],"LLE.":[48,102],"In":[49],"this":[50],"paper,":[51],"we":[52,79],"conduct":[53],"error":[55],"analysis":[56],"the":[58,74,85,89,92,99],"LLE":[59,67],"show":[62],"that":[63],"under":[64],"what":[65],"conditions":[66],"would":[68],"be":[69],"able":[70],"correctly":[72],"discover":[73],"underlying":[75],"manifold":[76],"structure.":[77],"Besides,":[78],"also":[80],"present":[81],"reconstruction":[82],"between":[84],"weights":[87],"in":[88],"ambient":[93],"space,":[94],"which":[95],"crucial":[97],"success":[100],"of":[101]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}