{"id":"https://openalex.org/W2902581929","doi":"https://doi.org/10.1109/icpr.2018.8545404","title":"A Linear Incremental Nystr\u00f6m Method for Online Kernel Learning","display_name":"A Linear Incremental Nystr\u00f6m Method for Online Kernel Learning","publication_year":2018,"publication_date":"2018-08-01","ids":{"openalex":"https://openalex.org/W2902581929","doi":"https://doi.org/10.1109/icpr.2018.8545404","mag":"2902581929"},"language":"en","primary_location":{"id":"doi:10.1109/icpr.2018.8545404","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icpr.2018.8545404","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 24th International Conference on Pattern Recognition (ICPR)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5101832588","display_name":"Shan Xu","orcid":"https://orcid.org/0000-0002-0072-2156"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shan Xu","raw_affiliation_strings":["School of Computer Science and Technology, Tianjin University, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Tianjin University, Tianjin, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100696673","display_name":"Xiao Zhang","orcid":"https://orcid.org/0000-0002-8020-6142"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiao Zhang","raw_affiliation_strings":["School of Computer Science and Technology, Tianjin University, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Tianjin University, Tianjin, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089843351","display_name":"Shizhong Liao","orcid":"https://orcid.org/0000-0003-0594-7116"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shizhong Liao","raw_affiliation_strings":["School of Computer Science and Technology, Tianjin University, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Tianjin University, Tianjin, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2256","last_page":"2261"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987999796867371,"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/T12676","display_name":"Machine Learning and ELM","score":0.9973999857902527,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6401495933532715},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.5185916423797607},{"id":"https://openalex.org/keywords/kernel-embedding-of-distributions","display_name":"Kernel embedding of distributions","score":0.5174344182014465},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"Polynomial kernel","score":0.4859291613101959},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.46921196579933167},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4679775536060333},{"id":"https://openalex.org/keywords/kernel-principal-component-analysis","display_name":"Kernel principal component analysis","score":0.428983598947525},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42627984285354614},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41782858967781067},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3492361903190613},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3348073363304138},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3011181354522705},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2883027195930481},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.2706388831138611},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1893143355846405}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6401495933532715},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.5185916423797607},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.5174344182014465},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.4859291613101959},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.46921196579933167},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4679775536060333},{"id":"https://openalex.org/C182335926","wikidata":"https://www.wikidata.org/wiki/Q17093020","display_name":"Kernel principal component analysis","level":4,"score":0.428983598947525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42627984285354614},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41782858967781067},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3492361903190613},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3348073363304138},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3011181354522705},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2883027195930481},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.2706388831138611},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1893143355846405},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icpr.2018.8545404","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icpr.2018.8545404","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 24th International Conference on Pattern Recognition (ICPR)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1497057245","https://openalex.org/W1999352252","https://openalex.org/W2012501405","https://openalex.org/W2107791152","https://openalex.org/W2110121428","https://openalex.org/W2112545207","https://openalex.org/W2154249783","https://openalex.org/W2160941318","https://openalex.org/W2185932763","https://openalex.org/W2286444068","https://openalex.org/W2344807909","https://openalex.org/W2408432900","https://openalex.org/W2513180554","https://openalex.org/W2561978763","https://openalex.org/W2608738262","https://openalex.org/W2609442768","https://openalex.org/W2612658493","https://openalex.org/W2951105225","https://openalex.org/W4205841652","https://openalex.org/W4244670803","https://openalex.org/W6676539569","https://openalex.org/W6686319040","https://openalex.org/W6704944720","https://openalex.org/W6714150371","https://openalex.org/W6736891279","https://openalex.org/W6737099590"],"related_works":["https://openalex.org/W2393746448","https://openalex.org/W1984421104","https://openalex.org/W2512565647","https://openalex.org/W2071590642","https://openalex.org/W2001772920","https://openalex.org/W2384322977","https://openalex.org/W2182834820","https://openalex.org/W2149803014","https://openalex.org/W2127229869","https://openalex.org/W2366185040"],"abstract_inverted_index":{"Although":[0],"the":[1,21,26,51,69,73,79,83,88,95,102,113,117,127,132,137,142,185,202,208,215],"incremental":[2,38,89,104,157,217],"Nystr\u00f6m":[3,39,105,158,218],"method":[4,106,159,178,219],"has":[5,160],"been":[6],"used":[7],"in":[8,43,224],"kernel":[9,17,65,109,114,139,147,166,181,225,233],"approximation,":[10,168],"it":[11],"is":[12,42,201,207,220,229],"not":[13],"suitable":[14,230],"for":[15,63,145,165,179,231],"online":[16,64,108,146,175,180,232],"learning":[18,148],"due":[19],"to":[20,50,107,194],"cubic":[22],"time":[23,46,186],"complexity":[24,47,187],"and":[25,57,93,125,183,205,222,228],"lack":[27],"of":[28,82,136,188],"theoretical":[29],"guarantees.":[30],"In":[31],"this":[32],"paper,":[33],"we":[34,111,153],"propose":[35],"a":[36,44,59,161,170],"novel":[37],"method,":[40],"which":[41],"linear":[45,143],"with":[48],"respect":[49],"sampling":[52,203],"size":[53,204],"at":[54,122,149,196],"each":[55,123,150,197],"round,":[56,124,198],"enjoys":[58,169],"sublinear":[60,171],"regret":[61,172],"bound":[62,164,173],"learning.":[66,234],"We":[67],"construct":[68],"intersection":[70,84],"matrix":[71,85,98,115,121,167,226],"using":[72,116,174],"ridge":[74],"leverage":[75],"score":[76],"estimator,":[77],"compute":[78],"rank-k":[80],"approximation":[81,227],"incrementally":[86],"via":[87],"singular":[90,133],"value":[91,134],"decomposition,":[92],"recalculate":[94],"generalized":[96,119,189],"inverse":[97,120,190],"periodically.":[99],"When":[100],"applying":[101],"proposed":[103,216],"learning,":[110,182],"approximate":[112],"updated":[118],"formulate":[126],"explicit":[128],"feature":[129],"mapping":[130],"by":[131],"decomposition":[135],"approximated":[138],"matrix,":[140],"yielding":[141],"classifier":[144],"round.":[151],"Theoretically,":[152],"prove":[154],"that":[155,214],"our":[156],"(1+\u03b5)":[162],"relative-error":[163],"gradient":[176],"descent":[177],"reduces":[184],"computation":[191],"from":[192],"O(m3)":[193],"O(mk)":[195],"where":[199],"m":[200],"k":[206],"truncated":[209],"rank.":[210],"Experimental":[211],"results":[212],"show":[213],"accurate":[221],"efficient":[223]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
