{"id":"https://openalex.org/W2023530265","doi":"https://doi.org/10.1109/tnnls.2012.2230406","title":"Generalization Performance of Fisher Linear Discriminant Based on Markov Sampling","display_name":"Generalization Performance of Fisher Linear Discriminant Based on Markov Sampling","publication_year":2012,"publication_date":"2012-12-24","ids":{"openalex":"https://openalex.org/W2023530265","doi":"https://doi.org/10.1109/tnnls.2012.2230406","mag":"2023530265","pmid":"https://pubmed.ncbi.nlm.nih.gov/24808282"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2012.2230406","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2012.2230406","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5078058840","display_name":"Bin Zou","orcid":"https://orcid.org/0000-0002-8649-1538"},"institutions":[{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bin Zou","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Hubei University, Wuhan, China","Fac. of Math. & Comput. Sci., Hubei Univ., Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Hubei University, Wuhan, China","institution_ids":["https://openalex.org/I75900474"]},{"raw_affiliation_string":"Fac. of Math. & Comput. Sci., Hubei Univ., Wuhan, China","institution_ids":["https://openalex.org/I75900474"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070570029","display_name":"Luoqing Li","orcid":"https://orcid.org/0000-0002-4770-2283"},"institutions":[{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Luoqing Li","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Hubei University, Wuhan, China","Fac. of Math. & Comput. Sci., Hubei Univ., Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Hubei University, Wuhan, China","institution_ids":["https://openalex.org/I75900474"]},{"raw_affiliation_string":"Fac. of Math. & Comput. Sci., Hubei Univ., Wuhan, China","institution_ids":["https://openalex.org/I75900474"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109280540","display_name":"Zongben Xu","orcid":"https://orcid.org/0000-0002-4066-2338"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zongben Xu","raw_affiliation_strings":["Institute for Information and System Science, Xi'an Jiaotong University, Xi'an, China","Inst. for Inf. & Syst. Sci., Xi'an Jiaotong Univ., Xi'an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Information and System Science, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Inst. for Inf. & Syst. Sci., Xi'an Jiaotong Univ., Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061844987","display_name":"Tao Luo","orcid":"https://orcid.org/0000-0003-2162-363X"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Luo","raw_affiliation_strings":["Institute for Information and System Science, Xi'an Jiaotong University, Xi'an, China","Inst. for Inf. & Syst. Sci., Xi'an Jiaotong Univ., Xi'an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Information and System Science, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Inst. for Inf. & Syst. Sci., Xi'an Jiaotong Univ., Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101981296","display_name":"Yuan Tang","orcid":"https://orcid.org/0000-0001-5243-233X"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Yuan Yan Tang","raw_affiliation_strings":["Faculty of Science and Technology, University of Macau, Macau, China","[Fac. of Sci. & Technol., Univ. of Macau, Macau, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science and Technology, University of Macau, Macau, China","institution_ids":["https://openalex.org/I204512498"]},{"raw_affiliation_string":"[Fac. of Sci. & Technol., Univ. of Macau, Macau, China]","institution_ids":["https://openalex.org/I204512498"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.5188,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.97073969,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"2","first_page":"288","last_page":"300"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9975000023841858,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9975000023841858,"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/T10057","display_name":"Face and Expression Recognition","score":0.994700014591217,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/markov-chain","display_name":"Markov chain","score":0.7534216046333313},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6189313530921936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5910046696662903},{"id":"https://openalex.org/keywords/linear-discriminant-analysis","display_name":"Linear discriminant analysis","score":0.5636045336723328},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5565636157989502},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.48529642820358276},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.45990774035453796},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4405355453491211},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.41123417019844055},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.401040256023407},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3884351849555969},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36735451221466064},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33762675523757935},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3338467478752136},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.16689804196357727}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7534216046333313},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6189313530921936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5910046696662903},{"id":"https://openalex.org/C69738355","wikidata":"https://www.wikidata.org/wiki/Q1228929","display_name":"Linear discriminant analysis","level":2,"score":0.5636045336723328},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5565636157989502},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.48529642820358276},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.45990774035453796},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4405355453491211},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.41123417019844055},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.401040256023407},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3884351849555969},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36735451221466064},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33762675523757935},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3338467478752136},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.16689804196357727},{"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/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2012.2230406","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2012.2230406","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:24808282","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/24808282","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.7300000190734863,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W1511018260","https://openalex.org/W1534477342","https://openalex.org/W1554944419","https://openalex.org/W1614659291","https://openalex.org/W1995713768","https://openalex.org/W2001619934","https://openalex.org/W2001960189","https://openalex.org/W2009754940","https://openalex.org/W2017332415","https://openalex.org/W2020999234","https://openalex.org/W2021440127","https://openalex.org/W2028548064","https://openalex.org/W2032882463","https://openalex.org/W2046649434","https://openalex.org/W2047278710","https://openalex.org/W2051203581","https://openalex.org/W2056392803","https://openalex.org/W2056760934","https://openalex.org/W2058402854","https://openalex.org/W2075672181","https://openalex.org/W2083875149","https://openalex.org/W2084134149","https://openalex.org/W2085535170","https://openalex.org/W2103012681","https://openalex.org/W2104290726","https://openalex.org/W2110455165","https://openalex.org/W2110652811","https://openalex.org/W2111574755","https://openalex.org/W2124161253","https://openalex.org/W2133551294","https://openalex.org/W2135194391","https://openalex.org/W2137611320","https://openalex.org/W2138309709","https://openalex.org/W2142563104","https://openalex.org/W2142623799","https://openalex.org/W2145527806","https://openalex.org/W2147303334","https://openalex.org/W2148603752","https://openalex.org/W2149614431","https://openalex.org/W2161712044","https://openalex.org/W2167998037","https://openalex.org/W2171033594","https://openalex.org/W2296685631","https://openalex.org/W2479575276","https://openalex.org/W2597289420","https://openalex.org/W2990138404","https://openalex.org/W3017143921","https://openalex.org/W3021787434","https://openalex.org/W3102676469","https://openalex.org/W4233372644","https://openalex.org/W4233413206","https://openalex.org/W4237826793","https://openalex.org/W4238240379","https://openalex.org/W4285719527","https://openalex.org/W4302434451","https://openalex.org/W7046297837"],"related_works":["https://openalex.org/W2794812819","https://openalex.org/W2114217318","https://openalex.org/W2587881214","https://openalex.org/W3104072235","https://openalex.org/W1995622179","https://openalex.org/W2048680804","https://openalex.org/W2370263288","https://openalex.org/W1484111231","https://openalex.org/W2169311637","https://openalex.org/W3192451249"],"abstract_inverted_index":{"Fisher":[0],"linear":[1],"discriminant":[2],"(FLD)":[3],"is":[4,99],"a":[5,18,115,126],"well-known":[6],"method":[7],"for":[8,119],"dimensionality":[9],"reduction":[10],"and":[11,46,91,135],"classification":[12],"that":[13,93,145],"projects":[14],"high-dimensional":[15],"data":[16,23,128],"onto":[17],"low-dimensional":[19],"space":[20],"where":[21],"the":[22,32,42,63,75,78,103],"achieves":[24],"maximum":[25],"class":[26],"separability.":[27],"The":[28],"previous":[29],"works":[30],"describing":[31],"generalization":[33,64,79],"ability":[34,65],"of":[35,44,66,81,129],"FLD":[36,67,82,94,120,146],"have":[37],"usually":[38],"been":[39],"based":[40,68,83,95,147],"on":[41,69,77,84,96,138,148],"assumption":[43],"independent":[45],"identically":[47],"distributed":[48],"(i.i.d.)":[49],"samples.":[50,163],"In":[51],"this":[52,58],"paper,":[53],"we":[54,112,143],"go":[55],"far":[56],"beyond":[57],"classical":[59],"framework":[60],"by":[61,152],"studying":[62],"Markov":[70,87,107,116,153],"sampling.":[71],"We":[72],"first":[73],"establish":[74],"bounds":[76],"performance":[80],"uniformly":[85],"ergodic":[86],"chain":[88,108],"(u.e.M.c.)":[89],"samples,":[90],"prove":[92],"u.e.M.c.":[97,123,149],"samples":[98,124,150],"consistent.":[100],"By":[101],"following":[102],"enlightening":[104],"idea":[105],"from":[106,125],"Monto":[109],"Carlo":[110],"methods,":[111],"also":[113],"introduce":[114],"sampling":[117,154],"algorithm":[118],"to":[121,161],"generate":[122],"given":[127],"finite":[130],"size.":[131],"Through":[132],"simulation":[133],"studies":[134,137],"numerical":[136],"benchmark":[139],"repository":[140],"using":[141],"FLD,":[142],"find":[144],"generated":[151],"can":[155],"provide":[156],"smaller":[157],"misclassification":[158],"rates":[159],"compared":[160],"i.i.d.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}