{"id":"https://openalex.org/W2072330436","doi":"https://doi.org/10.1145/1064092.1064125","title":"Provable dimension detection using principal component analysis","display_name":"Provable dimension detection using principal component analysis","publication_year":2005,"publication_date":"2005-06-06","ids":{"openalex":"https://openalex.org/W2072330436","doi":"https://doi.org/10.1145/1064092.1064125","mag":"2072330436"},"language":"en","primary_location":{"id":"doi:10.1145/1064092.1064125","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1064092.1064125","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-first annual symposium on Computational geometry","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/A5070497738","display_name":"Siu-Wing Cheng","orcid":"https://orcid.org/0000-0002-3557-9935"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Siu-Wing Cheng","raw_affiliation_strings":["HKUST, Hong Kong","[HKUST, Hong Kong]"],"affiliations":[{"raw_affiliation_string":"HKUST, Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"[HKUST, Hong Kong]","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100454894","display_name":"Yajun Wang","orcid":"https://orcid.org/0000-0002-9990-0812"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yajun Wang","raw_affiliation_strings":["HKUST, Hong Kong","[HKUST, Hong Kong]"],"affiliations":[{"raw_affiliation_string":"HKUST, Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"[HKUST, Hong Kong]","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103904217","display_name":"Zhuangzhi Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhuangzhi Wu","raw_affiliation_strings":["Beihang Univ., Beijing","Beihang University,Beijing"],"affiliations":[{"raw_affiliation_string":"Beihang Univ., Beijing","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Beihang University,Beijing","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070497738"],"corresponding_institution_ids":["https://openalex.org/I200769079"],"apc_list":null,"apc_paid":null,"fwci":0.6733,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.71971006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"208","last_page":"217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9993000030517578,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9851999878883362,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.6766995787620544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6386486291885376},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6372746229171753},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.6228147149085999},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5732396245002747},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.537307620048523},{"id":"https://openalex.org/keywords/intrinsic-dimension","display_name":"Intrinsic dimension","score":0.5286581516265869},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.46152985095977783},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4582791030406952},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.4448195993900299},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.4179174602031708},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40316131711006165},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.2555691599845886},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2389509677886963}],"concepts":[{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.6766995787620544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6386486291885376},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6372746229171753},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.6228147149085999},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5732396245002747},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.537307620048523},{"id":"https://openalex.org/C30732413","wikidata":"https://www.wikidata.org/wiki/Q17092636","display_name":"Intrinsic dimension","level":3,"score":0.5286581516265869},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.46152985095977783},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4582791030406952},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.4448195993900299},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.4179174602031708},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40316131711006165},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.2555691599845886},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2389509677886963}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/1064092.1064125","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1064092.1064125","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-first annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1010.4147","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1010.4147","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Zhuangzhi_Wu/publication/220669842_Provable_Dimension_Detection_Using_Principal_Component_Analysis/links/00b7d52ceb4af0ba41000000.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1020.6780","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1020.6780","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Zhuangzhi_Wu/publication/220983754_Provable_dimension_detection_using_principal_component_analysis/links/00b7d52ceb4aea7b05000000.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.97.9762","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.97.9762","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ust.hk/~scheng/pub/dimension.pdf","raw_type":"text"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-27645","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-27645","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Conference paper"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5600000023841858,"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":24,"referenced_works":["https://openalex.org/W120774042","https://openalex.org/W2001141328","https://openalex.org/W2014530345","https://openalex.org/W2020065037","https://openalex.org/W2022266599","https://openalex.org/W2028569884","https://openalex.org/W2029041800","https://openalex.org/W2051200663","https://openalex.org/W2059586807","https://openalex.org/W2083485913","https://openalex.org/W2083493892","https://openalex.org/W2088352159","https://openalex.org/W2094383180","https://openalex.org/W2106209520","https://openalex.org/W2119513586","https://openalex.org/W2125511726","https://openalex.org/W2148694408","https://openalex.org/W2162618853","https://openalex.org/W2203555918","https://openalex.org/W2313673092","https://openalex.org/W2798909945","https://openalex.org/W3139066715","https://openalex.org/W4292023222","https://openalex.org/W6671164174"],"related_works":["https://openalex.org/W2113270940","https://openalex.org/W2004283824","https://openalex.org/W4389469802","https://openalex.org/W1581210843","https://openalex.org/W1982530285","https://openalex.org/W1992104669","https://openalex.org/W2521054645","https://openalex.org/W4308615710","https://openalex.org/W1998702677","https://openalex.org/W4287027197"],"abstract_inverted_index":{"We":[0],"present":[1],"simple":[2],"algorithms":[3],"for":[4,66],"detecting":[5],"the":[6,51,62,74,94,101,109,118,129],"dimension":[7,76],"k":[8],"of":[9,20,96,128],"a":[10,17,27,125],"smooth":[11],"manifold":[12],"M":[13],"\u2282":[14],"Rd":[15],"from":[16],"set":[18],"P":[19,25],"point":[21],"samples,":[22],"provided":[23],"that":[24,107],"satisfies":[26],"standard":[28],"sampling":[29],"condition":[30],"as":[31],"in":[32,57,82,99,121],"previous":[33],"results.":[34],"The":[35],"best":[36],"running":[37],"time":[38],"so":[39],"far":[40],"is":[41,55,106],"O(d2O(k7":[42],"log":[43,86],"k))":[44],"worst-case":[45,59],"by":[46],"Giesen":[47],"and":[48,111,124],"Wagner":[49],"after":[50],"adaptive":[52,63],"neighborhood":[53,64],"graph":[54],"constructed":[56],"O(d|P|2)":[58],"time.":[60,89],"Given":[61],"graph,":[65],"any":[67],"l":[68,85],"\u2265":[69],"1,":[70],"our":[71,97],"algorithm":[72,110],"outputs":[73],"true":[75],"with":[77],"probability":[78],"at":[79],"least":[80],"1-2-l":[81],"O(2O(k)kd(k":[83],"+":[84],"d))":[87],"expected":[88],"Our":[90],"experimental":[91],"results":[92],"validate":[93],"effectiveness":[95],"approach":[98],"computing":[100],"dimension.":[102],"A":[103],"further":[104],"advantage":[105],"both":[108],"its":[112],"analysis":[113],"can":[114],"be":[115],"generalized":[116],"to":[117],"noisy":[119],"case,":[120],"which":[122],"outliers":[123],"small":[126],"perturbation":[127],"samples":[130],"are":[131],"allowed.":[132]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}