{"id":"https://openalex.org/W2988585396","doi":null,"title":"Efficient Ridge Solutions for the Incremental Broad Learning System on Added Inputs by Updating the Inverse or the Inverse Cholesky Factor of the Hermitian matrix in the Ridge Inverse.","display_name":"Efficient Ridge Solutions for the Incremental Broad Learning System on Added Inputs by Updating the Inverse or the Inverse Cholesky Factor of the Hermitian matrix in the Ridge Inverse.","publication_year":2019,"publication_date":"2019-11-12","ids":{"openalex":"https://openalex.org/W2988585396","mag":"2988585396"},"language":"en","primary_location":{"id":"mag:2988585396","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1911.07292.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1911.07292.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039864918","display_name":"Hufei Zhu","orcid":"https://orcid.org/0000-0002-1629-6227","observed_orcids":["https://orcid.org/0000-0002-1629-6227"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hufei Zhu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-1629-6227","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110648392","display_name":"Chenghao Wei","orcid":"https://orcid.org/0009-0009-6172-0486","observed_orcids":["https://orcid.org/0009-0009-6172-0486"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chenghao Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"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":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.9272000193595886,"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":0.9272000193595886,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.04390000179409981,"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/T10320","display_name":"Neural Networks and Applications","score":0.008899999782443047,"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/hermitian-matrix","display_name":"Hermitian matrices","score":0.8450000286102295},{"id":"https://openalex.org/keywords/matrix-inversion-lemma","display_name":"matrix inversion lemma","score":0.9760000109672546},{"id":"https://openalex.org/keywords/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.8529999852180481},{"id":"https://openalex.org/keywords/computational-efficiency","display_name":"computational efficiency","score":0.6809999942779541},{"id":"https://openalex.org/keywords/floating-point-operations","display_name":"floating-point operations","score":0.8370000123977661},{"id":"https://openalex.org/keywords/training-acceleration","display_name":"training acceleration","score":0.40700000524520874}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.9608182311058044},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.7343407869338989},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7051013708114624},{"id":"https://openalex.org/C46085209","wikidata":"https://www.wikidata.org/wiki/Q17098969","display_name":"Minimum degree algorithm","level":5,"score":0.7035311460494995},{"id":"https://openalex.org/C3826847","wikidata":"https://www.wikidata.org/wiki/Q188768","display_name":"FLOPS","level":2,"score":0.5773494243621826},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.5574392676353455},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.554487407207489},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5081751346588135},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4717617332935333},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4561365246772766},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3946232795715332},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33160465955734253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31934648752212524},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09338077902793884},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.08941462635993958},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08300349116325378},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2988585396","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1911.07292.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2988585396","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1911.07292.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1573981097","https://openalex.org/W1980568723","https://openalex.org/W1996640396","https://openalex.org/W2012638612","https://openalex.org/W2043005456","https://openalex.org/W2080102365","https://openalex.org/W2104849640","https://openalex.org/W2112796928","https://openalex.org/W2154579312","https://openalex.org/W2157475639","https://openalex.org/W2738226240","https://openalex.org/W2890126432","https://openalex.org/W2980727528"],"related_works":["https://openalex.org/W3214899170","https://openalex.org/W3180126314","https://openalex.org/W3164448675","https://openalex.org/W2980727528","https://openalex.org/W4397003385","https://openalex.org/W3024033942","https://openalex.org/W4386397730","https://openalex.org/W3115148317","https://openalex.org/W4399991085","https://openalex.org/W4405305453"],"abstract_inverted_index":{"This":[0],"brief":[1],"proposes":[2],"two":[3],"BLS":[4,10,19,53,82,210,240],"algorithms":[5,20,198,241],"to":[6,115,154],"improve":[7],"the":[8,23,28,32,36,39,44,48,57,60,64,71,77,80,86,109,116,128,135,144,156,165,177,182,186,192,196,208,216,223,226,238,246,259,262],"existing":[9,209,247],"for":[11,225,261],"new":[12],"added":[13,111,117,131],"inputs":[14,118],"in":[15,47,164,176,185,232],"[7].":[16],"The":[17,51],"proposed":[18,52,81,166,178,197,239],"avoid":[21],"computing":[22,27],"ridge":[24,29,49,187,193],"inverse,":[25],"by":[26,63,98,159,170,215],"solution":[30],"(i.e.,":[31],"output":[33],"weights)":[34],"from":[35],"inverse":[37,40,58,73,87,104,145,163,173,188],"or":[38,102,169],"Cholesky":[41,74,88,100,105,174],"factor":[42,75,89],"of":[43,59,76,130,146,149,228,237,264],"Hermitian":[45,61,78,183],"matrix":[46,62,65,113,162,184],"inverse.":[50,194],"algorithm":[54,83,167,179,248],"1":[55,199,242],"updates":[56],"inversion":[66],"lemma":[67],"[12].":[68],"To":[69],"update":[70],"upper-triangular":[72,92],"matrix,":[79,94],"2":[84,201,244],"multiplies":[85],"with":[90],"an":[91,103],"intermediate":[93,157],"which":[95,212],"is":[96,119,152,189,213],"computed":[97],"a":[99,147,160,171],"factorization":[101,175],"factorization.":[106],"Assume":[107],"that":[108],"newly":[110],"input":[112],"corresponding":[114],"p":[120,124,141,229,265],"*":[121],"k,":[122,143],"where":[123],"and":[125,134,200,243,253,258,272],"k":[126,231,267],"are":[127,249,268],"number":[129],"training":[132,235],"samples":[133],"total":[136],"node":[137],"number,":[138],"respectively.":[139,276],"When":[140],">":[142,230],"sum":[148],"matrices":[150],"[11]":[151],"utilized":[153],"compute":[155],"variables":[158],"smaller":[161,172,190],"1,":[168],"2.":[180],"Usually":[181],"than":[191,207],"Thus":[195],"require":[202],"less":[203],"flops":[204,218],"(floating-point":[205],"operations)":[206],"algorithm,":[211],"verified":[214],"theoretical":[217],"calculation.":[219],"In":[220],"numerical":[221],"experiments,":[222],"speedups":[224,260],"case":[227,263],"each":[233],"additional":[234],"time":[236],"over":[245],"1.95":[250],"-":[251,255,270,274],"5.43":[252],"2.29":[254],"6.34,":[256],"respectively,":[257],"<":[266],"8.83":[269],"10.21":[271],"2.28":[273],"2.58,":[275]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-09-26T08:19:03.415552","created_date":"2019-11-22T00:00:00"}
