{"id":"https://openalex.org/W3045171887","doi":"https://doi.org/10.1109/lsp.2020.3011323","title":"Capped $\\ell _p$-Norm LDA for Outliers Robust Dimension Reduction","display_name":"Capped $\\ell _p$-Norm LDA for Outliers Robust Dimension Reduction","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3045171887","doi":"https://doi.org/10.1109/lsp.2020.3011323","mag":"3045171887"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2020.3011323","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2020.3011323","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-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/A5100401102","display_name":"Zheng Wang","orcid":"https://orcid.org/0000-0002-4814-1115"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zheng Wang","raw_affiliation_strings":["School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi\u2019an, China","School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0002-4814-1115","affiliations":[{"raw_affiliation_string":"School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003222421","display_name":"Feiping Nie","orcid":"https://orcid.org/0000-0002-0871-6519"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feiping Nie","raw_affiliation_strings":["School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi\u2019an, China","School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0002-0871-6519","affiliations":[{"raw_affiliation_string":"School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021971528","display_name":"Canyu Zhang","orcid":"https://orcid.org/0000-0003-4660-6772"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Canyu Zhang","raw_affiliation_strings":["School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi\u2019an, China","School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030351224","display_name":"Rong Wang","orcid":"https://orcid.org/0000-0001-9240-6726"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rong Wang","raw_affiliation_strings":["School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi\u2019an, China","School of Cybersecurity, Northwestern Polytechnical University, Xi\u2019an, China","School of Cybersecurity, Northwestern Polytechnical University, Xi'an, China","School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0001-9240-6726","affiliations":[{"raw_affiliation_string":"School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Cybersecurity, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Cybersecurity, Northwestern Polytechnical University, Xi'an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106943753","display_name":"Xuelong Li","orcid":"https://orcid.org/0000-0003-2924-946X"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuelong Li","raw_affiliation_strings":["School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi\u2019an, China","School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Computer Science and Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, China","institution_ids":["https://openalex.org/I17145004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":null,"apc_paid":null,"fwci":2.167,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.90154901,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"27","issue":null,"first_page":"1315","last_page":"1319"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9997000098228455,"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9997000098228455,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9944000244140625,"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"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9939000010490417,"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":0.7999558448791504},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6896864175796509},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.625243067741394},{"id":"https://openalex.org/keywords/linear-discriminant-analysis","display_name":"Linear discriminant analysis","score":0.5353641510009766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5169134140014648},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.509674072265625},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4715433418750763},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4550406336784363},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39645856618881226},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3771156370639801},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.35538965463638306}],"concepts":[{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.7999558448791504},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6896864175796509},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.625243067741394},{"id":"https://openalex.org/C69738355","wikidata":"https://www.wikidata.org/wiki/Q1228929","display_name":"Linear discriminant analysis","level":2,"score":0.5353641510009766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5169134140014648},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.509674072265625},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4715433418750763},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4550406336784363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39645856618881226},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3771156370639801},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.35538965463638306},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2020.3011323","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2020.3011323","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.75,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1537487564","display_name":"\u7ed3\u6784\u5316\u56fe\u5b66\u4e60\u7406\u8bba\u4e0e\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61772427","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2416935669","display_name":null,"funder_award_id":"2018YFB1403501","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3280333285","display_name":null,"funder_award_id":"G2019KY0501","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G653700208","display_name":null,"funder_award_id":"61751202","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7761990065","display_name":null,"funder_award_id":"61936014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1501378864","https://openalex.org/W1576613474","https://openalex.org/W1603382914","https://openalex.org/W1979089718","https://openalex.org/W2007312210","https://openalex.org/W2008277111","https://openalex.org/W2009835454","https://openalex.org/W2053090063","https://openalex.org/W2073117966","https://openalex.org/W2105055468","https://openalex.org/W2133538634","https://openalex.org/W2151416140","https://openalex.org/W2153051254","https://openalex.org/W2164958105","https://openalex.org/W2516176725","https://openalex.org/W2543969232","https://openalex.org/W2595698050","https://openalex.org/W2736675202","https://openalex.org/W2750378047","https://openalex.org/W2792434637","https://openalex.org/W2807548733","https://openalex.org/W2941129248","https://openalex.org/W2945223572","https://openalex.org/W2966893608","https://openalex.org/W2997973367","https://openalex.org/W3004545648","https://openalex.org/W3010790568","https://openalex.org/W3023058184","https://openalex.org/W3035396932","https://openalex.org/W4298082496","https://openalex.org/W6634500723","https://openalex.org/W6682602143","https://openalex.org/W6749438310"],"related_works":["https://openalex.org/W2794812819","https://openalex.org/W2114217318","https://openalex.org/W2587881214","https://openalex.org/W3104072235","https://openalex.org/W2048680804","https://openalex.org/W2370263288","https://openalex.org/W2169311637","https://openalex.org/W3192451249","https://openalex.org/W4367850163","https://openalex.org/W2395040056"],"abstract_inverted_index":{"Linear":[0],"discriminant":[1],"analysis":[2],"technique":[3],"is":[4,129],"an":[5,135],"effective":[6],"strategy":[7],"to":[8,33,78,95,141,170],"solve":[9],"the":[10,14,29,38,48,54,67,101,111,117,126,143,167],"long-standing":[11],"issue,":[12,75],"i.e.,":[13],"\u201ccurse":[15],"of":[16,172],"dimensionality\u201d":[17],"that":[18],"brings":[19],"many":[20,51],"obstacles":[21],"on":[22,66,147,161],"high-dimensional":[23],"data":[24],"storage":[25],"and":[26,69,163],"analysis.":[27],"However,":[28],"projections":[30],"are":[31],"prone":[32],"be":[34],"affected,":[35],"especially":[36],"when":[37],"training":[39,127],"set":[40,128],"contains":[41],"outlier":[42,55],"samples":[43,56],"whose":[44],"distribution":[45],"deviates":[46],"from":[47],"globality.":[49],"In":[50],"real-world":[52,164],"applications,":[53],"contaminated":[57,130],"by":[58],"noisy":[59],"signal":[60],"or":[61],"spottiness":[62],"have":[63],"negative":[64],"effects":[65],"classification":[68],"clustering":[70],"performance.":[71],"To":[72],"address":[73],"this":[74],"we":[76,133],"propose":[77],"develop":[79],"a":[80],"novel":[81],"capped":[82,102,148],"\u2113":[83,103,149],"<sub":[84,104,150],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[85,105,151],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</sub>":[86,106,152],"-norm":[87,107,153],"LDA":[88],"model":[89],"for":[90],"robust":[91],"dimension":[92],"reduction":[93],"against":[94,169],"outliers":[96,119,171],"specifically.":[97],"Proposed":[98],"method":[99],"integrates":[100],"based":[108,146],"loss":[109],"into":[110],"objective,":[112],"which":[113],"not":[114],"only":[115],"suppresses":[116],"light":[118],"but":[120],"also":[121],"works":[122],"well":[123],"even":[124],"though":[125],"seriously.":[131],"Furthermore,":[132],"derive":[134],"alternative":[136],"iterative":[137],"re-weighted":[138],"optimization":[139],"algorithm":[140],"minimize":[142],"proposed":[144,173],"objective":[145],"with":[154],"rigorous":[155],"convergence":[156],"proofs.":[157],"Extensive":[158],"experiments":[159],"conducted":[160],"synthetic":[162],"datasets":[165],"demonstrate":[166],"robustness":[168],"method.":[174]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}