{"id":"https://openalex.org/W2972958113","doi":"https://doi.org/10.1109/tnnls.2019.2935502","title":"Probability Density Rank-Based Quantization for Convex Universal Learning Machines","display_name":"Probability Density Rank-Based Quantization for Convex Universal Learning Machines","publication_year":2019,"publication_date":"2019-09-12","ids":{"openalex":"https://openalex.org/W2972958113","doi":"https://doi.org/10.1109/tnnls.2019.2935502","mag":"2972958113","pmid":"https://pubmed.ncbi.nlm.nih.gov/31536021"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2019.2935502","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2019.2935502","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/A5027468923","display_name":"Zhengda Qin","orcid":"https://orcid.org/0000-0002-7329-6936"},"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":true,"raw_author_name":"Zhengda Qin","raw_affiliation_strings":["School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, China","School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077852542","display_name":"Badong Chen","orcid":"https://orcid.org/0000-0003-1710-3818"},"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":"Badong Chen","raw_affiliation_strings":["School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, China","School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100621681","display_name":"Yuantao Gu","orcid":"https://orcid.org/0000-0002-8427-1021"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuantao Gu","raw_affiliation_strings":["Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, China","Department of Electronic Engineering, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047405956","display_name":"Nanning Zheng","orcid":"https://orcid.org/0000-0003-1608-8257"},"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":"Nanning Zheng","raw_affiliation_strings":["School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, China","School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019504861","display_name":"Jos\u00e9 C. Pr\u0131\u0301ncipe","orcid":"https://orcid.org/0000-0002-3449-3531"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jose C. Principe","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Florida, Gainesville, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Florida, Gainesville, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5027468923"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":null,"apc_paid":null,"fwci":1.4002,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.86472297,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"31","issue":"8","first_page":"3100","last_page":"3113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":1.0,"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/T12676","display_name":"Machine Learning and ELM","score":1.0,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.996999979019165,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9955999851226807,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.5397670269012451},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.531123161315918},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.525997519493103},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4947814345359802},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41447755694389343},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.39491355419158936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39014315605163574}],"concepts":[{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.5397670269012451},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.531123161315918},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.525997519493103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4947814345359802},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41447755694389343},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.39491355419158936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39014315605163574}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2019.2935502","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2019.2935502","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:31536021","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31536021","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":[],"awards":[{"id":"https://openalex.org/G440816782","display_name":null,"funder_award_id":"91648208","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5668957906","display_name":null,"funder_award_id":"2015CB351703","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program 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}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":79,"referenced_works":["https://openalex.org/W65738273","https://openalex.org/W113793858","https://openalex.org/W176909285","https://openalex.org/W1480376833","https://openalex.org/W1483015037","https://openalex.org/W1492499319","https://openalex.org/W1551209770","https://openalex.org/W1558808826","https://openalex.org/W1571599052","https://openalex.org/W1601906285","https://openalex.org/W1634005169","https://openalex.org/W1819447595","https://openalex.org/W1967934524","https://openalex.org/W1970576574","https://openalex.org/W2009326110","https://openalex.org/W2011197824","https://openalex.org/W2021231414","https://openalex.org/W2024812658","https://openalex.org/W2050913223","https://openalex.org/W2055674909","https://openalex.org/W2071820974","https://openalex.org/W2074429597","https://openalex.org/W2082624758","https://openalex.org/W2097021318","https://openalex.org/W2105608756","https://openalex.org/W2111072639","https://openalex.org/W2112545207","https://openalex.org/W2116810533","https://openalex.org/W2119334829","https://openalex.org/W2125525099","https://openalex.org/W2125865219","https://openalex.org/W2126751256","https://openalex.org/W2128448396","https://openalex.org/W2129905273","https://openalex.org/W2134383396","https://openalex.org/W2134901991","https://openalex.org/W2135186252","https://openalex.org/W2135346934","https://openalex.org/W2135505249","https://openalex.org/W2137199074","https://openalex.org/W2137557016","https://openalex.org/W2141372707","https://openalex.org/W2144902422","https://openalex.org/W2145937819","https://openalex.org/W2150738795","https://openalex.org/W2151738995","https://openalex.org/W2160840682","https://openalex.org/W2164943005","https://openalex.org/W2169931829","https://openalex.org/W2171792531","https://openalex.org/W2307132432","https://openalex.org/W2342654477","https://openalex.org/W2414747154","https://openalex.org/W2532798880","https://openalex.org/W2533726396","https://openalex.org/W2599272755","https://openalex.org/W2616038372","https://openalex.org/W2734874104","https://openalex.org/W2738226240","https://openalex.org/W2913399920","https://openalex.org/W2922084435","https://openalex.org/W2963976431","https://openalex.org/W3105846425","https://openalex.org/W4233014035","https://openalex.org/W4247379750","https://openalex.org/W4256757978","https://openalex.org/W4285719527","https://openalex.org/W6604607589","https://openalex.org/W6632758585","https://openalex.org/W6634941687","https://openalex.org/W6635850547","https://openalex.org/W6678814708","https://openalex.org/W6680440628","https://openalex.org/W6680634009","https://openalex.org/W6681302627","https://openalex.org/W6682376617","https://openalex.org/W6685152693","https://openalex.org/W6715570297","https://openalex.org/W6748213982"],"related_works":["https://openalex.org/W2961085424","https://openalex.org/W4306674287","https://openalex.org/W4387369504","https://openalex.org/W3046775127","https://openalex.org/W4394896187","https://openalex.org/W3170094116","https://openalex.org/W4386462264","https://openalex.org/W3107602296","https://openalex.org/W4364306694","https://openalex.org/W4312192474"],"abstract_inverted_index":{"The":[0,19,85,135,201],"distributions":[1],"of":[2,24,44,52,83,133,143,198,217],"input":[3],"data":[4,89,109,144,151,167,210],"are":[5,21,103,129],"very":[6],"important":[7],"for":[8,164],"learning":[9,16,26],"machines,":[10],"such":[11],"as":[12],"the":[13,32,42,45,53,80,88,92,107,113,141,147,156,161,169,180,188,199],"convex":[14,29],"universal":[15,25],"machines":[17,27],"(CULMs).":[18],"CULMs":[20,54],"a":[22,36,99,165],"family":[23],"with":[28,220],"optimization.":[30],"However,":[31],"computational":[33,81,157],"complexity":[34,82],"is":[35,55,204],"crucial":[37],"problem":[38],"in":[39,59,106,187],"CULMs,":[40],"because":[41],"dimension":[43],"nonlinear":[46],"mapping":[47],"layer":[48],"(the":[49],"hidden":[50],"layer)":[51],"usually":[56],"rather":[57],"large":[58],"complex":[60],"system":[61],"modeling.":[62],"In":[63],"this":[64],"article,":[65],"we":[66],"propose":[67],"an":[68],"efficient":[69],"quantization":[70,173],"method":[71,137,170],"called":[72],"Probability":[73],"density":[74],"Rank-based":[75],"Quantization":[76],"(PRQ)":[77],"to":[78,91,115,195],"decrease":[79],"CULMs.":[84,134,200],"PRQ":[86,114,203,218],"ranks":[87],"according":[90],"estimated":[93],"probability":[94],"densities":[95],"and":[96,120,150,175,182],"then":[97],"selects":[98],"subset":[100],"whose":[101],"elements":[102],"equally":[104],"spaced":[105],"ranked":[108],"sequence.":[110],"We":[111],"apply":[112],"kernel":[116],"ridge":[117],"regression":[118],"(KRR)":[119],"random":[121],"Fourier":[122],"feature":[123],"recursive":[124],"least":[125],"squares":[126],"(RFF-RLS),":[127],"which":[128],"two":[130],"typical":[131],"algorithms":[132],"proposed":[136,202],"not":[138],"only":[139],"keeps":[140],"similarity":[142],"distribution":[145],"between":[146],"code":[148,189],"book":[149],"set":[152],"but":[153],"also":[154,178],"reduces":[155],"cost":[158],"by":[159],"using":[160],"kd-tree.":[162],"Meanwhile,":[163],"given":[166],"set,":[168],"yields":[171],"deterministic":[172],"results,":[174],"it":[176],"can":[177],"exclude":[179],"outliers":[181],"avoid":[183],"too":[184],"many":[185],"borders":[186],"book.":[190],"This":[191],"brings":[192],"great":[193],"convenience":[194],"practical":[196],"applications":[197],"evaluated":[205],"on":[206],"several":[207],"real-world":[208],"benchmark":[209],"sets.":[211],"Experimental":[212],"results":[213],"show":[214],"satisfactory":[215],"performance":[216],"compared":[219],"some":[221],"state-of-the-art":[222],"methods.":[223]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}