Convergence Analysis of Batch Gradient Algorithm for Three Classes of Sigma-Pi Neural Networks
Sigma-Pi (Σ-Π) neural networks (SPNNs) are known to provide more powerful mapping capability than traditional feed-forward neural networks. A unified convergence analysis for the batch gradient algorithm for SPNN learning is presented, covering three classes of SPNNs: Σ-Π-Σ, Σ-Σ-Π and Σ-Π-Σ-Π. The m...
Uložené v:
| Vydané v: | Neural processing letters Ročník 26; číslo 3; s. 177 - 189 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Dordrecht
Springer
01.12.2007
Springer Nature B.V |
| Predmet: | |
| ISSN: | 1370-4621, 1573-773X |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | Sigma-Pi (Σ-Π) neural networks (SPNNs) are known to provide more powerful mapping capability than traditional feed-forward neural networks. A unified convergence analysis for the batch gradient algorithm for SPNN learning is presented, covering three classes of SPNNs: Σ-Π-Σ, Σ-Σ-Π and Σ-Π-Σ-Π. The monotonicity of the error function in the iteration is also guaranteed. |
|---|---|
| AbstractList | Sigma-Pi (Σ-Π) neural networks (SPNNs) are known to provide more powerful mapping capability than traditional feed-forward neural networks. A unified convergence analysis for the batch gradient algorithm for SPNN learning is presented, covering three classes of SPNNs: Σ-Π-Σ, Σ-Σ-Π and Σ-Π-Σ-Π. The monotonicity of the error function in the iteration is also guaranteed. |
| Author | Xiong, Yan Wu, Wei Zhang, Chao |
| Author_xml | – sequence: 1 givenname: Chao surname: Zhang fullname: Zhang, Chao – sequence: 2 givenname: Wei surname: Wu fullname: Wu, Wei – sequence: 3 givenname: Yan surname: Xiong fullname: Xiong, Yan |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19212145$$DView record in Pascal Francis |
| BookMark | eNp9kE9Lw0AUxBdRsK1-AG8L4nF1_ySb5FiDVqGoYAVPhpdkt92aZuvuVum3N7EFwYOnmcNvhvdmiA5b2yqEzhi9ZJQmV54xKgXpLMloTAk9QAMWJ4IkiXg97LxIKIkkZ8do6P2S0i7F6QC95bb9VG6u2krhcQvN1huPrcbXEKoFnjiojWoDHjdz60xYrLC2Ds8WTimcN-C9-qGfzXwF5MngB7Vx0HQSvqx79yfoSEPj1eleR-jl9maW35Hp4-Q-H09JJWQWSMp5KWupa00jGYuIac3TMuYRq0UGaS2kTGIdxQzKUleCKaqAlSrKMoilLKkYofNd79rZj43yoVjajeve8QXPWCpEylPeURd7CnwFjXbQVsYXa2dW4LYFyzjjLIo7ju24ylnvndK_CC36uYvd3EVv-7mL_oLkT6YyAYKxbXBgmn-S37hChQ0 |
| CitedBy_id | crossref_primary_10_1007_s11063_011_9193_x crossref_primary_10_1016_j_neucom_2017_06_057 crossref_primary_10_1016_j_neucom_2012_02_029 crossref_primary_10_1109_TNNLS_2018_2846646 crossref_primary_10_1016_j_advwatres_2012_05_016 crossref_primary_10_1109_TNN_2011_2114367 crossref_primary_10_1007_s41066_023_00368_z crossref_primary_10_1587_transinf_2016EDP7152 crossref_primary_10_1007_s11063_013_9305_x crossref_primary_10_1007_s11571_013_9276_7 |
| Cites_doi | 10.1109/9.402231 10.1109/TNN.2005.844903 10.7551/mitpress/5236.001.0001 10.1162/neco.1989.1.1.133 10.1016/0893-6080(94)90009-4 10.1016/S0925-2312(01)00576-8 10.1016/j.neucom.2004.05.004 10.1023/A:1016249727555 10.1109/ICNNB.2005.1614626 10.1109/72.392251 |
| ContentType | Journal Article |
| Copyright | 2008 INIST-CNRS Copyright Springer Nature B.V. Dec 2007 |
| Copyright_xml | – notice: 2008 INIST-CNRS – notice: Copyright Springer Nature B.V. Dec 2007 |
| DBID | AAYXX CITATION IQODW 8FE 8FG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PSYQQ |
| DOI | 10.1007/s11063-007-9050-0 |
| DatabaseName | CrossRef Pascal-Francis ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials - QC ProQuest Central Technology collection ProQuest One Community College ProQuest Central ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Proquest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China ProQuest One Psychology |
| DatabaseTitle | CrossRef Advanced Technologies & Aerospace Collection ProQuest One Psychology Computer Science Database ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection ProQuest One Academic Eastern Edition SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central Advanced Technologies & Aerospace Database ProQuest One Applied & Life Sciences ProQuest One Academic UKI Edition ProQuest Central Korea ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Advanced Technologies & Aerospace Collection |
| Database_xml | – sequence: 1 dbid: P5Z name: Advanced Technologies & Aerospace Database url: https://search.proquest.com/hightechjournals sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science Applied Sciences |
| EISSN | 1573-773X |
| EndPage | 189 |
| ExternalDocumentID | 19212145 10_1007_s11063_007_9050_0 |
| GroupedDBID | -Y2 -~C .86 .DC .VR 06D 0R~ 0VY 123 1N0 203 29N 2J2 2JY 2KG 2LR 2VQ 2~H 30V 4.4 406 408 409 40D 40E 53G 5VS 67Z 6NX 77I 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AAHNG AAIAL AAJKR AAJSJ AAKKN AANZL AARHV AARTL AASML AATVU AAWCG AAYIU AAYQN AAYTO AAYXX ABBBX ABBXA ABDBE ABDZT ABECU ABEEZ ABFSG ABFTD ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABWNU ABXPI ACBXY ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACSNA ACSTC ADHHG ADHIR ADHKG ADIMF ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AENEX AEOHA AEPYU AETLH AEVLU AEXYK AEZWR AFBBN AFFHD AFGCZ AFGXO AFHIU AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGQPQ AGRTI AGWIL AGWZB AGYKE AHBYD AHKAY AHPBZ AHSBF AHWEU AHYZX AIAKS AIIXL AILAN AITGF AIXLP AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AYFIA AYJHY AZFZN B-. BA0 BDATZ BENPR BGLVJ BGNMA C6C CAG CCPQU CITATION COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ7 GQ8 GXS HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IXE IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K7- KDC KOV LAK LLZTM M4Y MA- N2Q NB0 NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9O PF0 PHGZM PHGZT PQGLB PSYQQ PT5 QOK QOS R89 R9I RHV RNS ROL RPX RSV S16 S27 S3B SAP SDH SDM SHX SISQX SNE SNPRN SNX SOHCF SOJ SPH SPISZ SRMVM SSLCW STPWE SZN T13 TEORI TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 ZMTXR ~EX 1SB 2.D 28- 2P1 5QI AAOBN AAUYE AAYZH ACACY ACULB AEFIE AESKC AFEXP AGGDS AHAVH BBWZM C24 H13 IQODW KOW NDZJH R4E RNI RZC RZE RZK S1Z S26 S28 SCJ SCLPG T16 8FE 8FG AZQEC DWQXO GNUQQ JQ2 P62 PKEHL PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c369t-822b6d6fdf0465341ff28b5241d39a8d36675f451abbfc31e0ea1be499a566b03 |
| IEDL.DBID | K7- |
| ISICitedReferencesCount | 12 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000250407900003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1370-4621 |
| IngestDate | Sat Oct 18 23:08:48 EDT 2025 Mon Jul 21 09:16:03 EDT 2025 Tue Nov 18 21:51:52 EST 2025 Sat Nov 29 02:27:44 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Sigma-Pi-Sigma-Pi neural networks, Batch gradient algorithm Gradient Error function 74P05 Monotonicity, 92B20 Neural network Sigma-Sigma-Pi neural networks Search algorithm Batch process Batch production Convergence, Sigma-Pi-Sigma neural networks Learning algorithm Artificial intelligence 68Q32 Algorithm analysis Monotonicity |
| Language | English |
| License | http://www.springer.com/tdm CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c369t-822b6d6fdf0465341ff28b5241d39a8d36675f451abbfc31e0ea1be499a566b03 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2918338282 |
| PQPubID | 2043838 |
| PageCount | 13 |
| ParticipantIDs | proquest_journals_2918338282 pascalfrancis_primary_19212145 crossref_primary_10_1007_s11063_007_9050_0 crossref_citationtrail_10_1007_s11063_007_9050_0 |
| PublicationCentury | 2000 |
| PublicationDate | 2007-12-01 |
| PublicationDateYYYYMMDD | 2007-12-01 |
| PublicationDate_xml | – month: 12 year: 2007 text: 2007-12-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | Dordrecht |
| PublicationPlace_xml | – name: Dordrecht |
| PublicationTitle | Neural processing letters |
| PublicationYear | 2007 |
| Publisher | Springer Springer Nature B.V |
| Publisher_xml | – name: Springer – name: Springer Nature B.V |
| References | JY Li (9050_CR2) 1995; 23 HM Shao (9050_CR6) 2004; 2 B Lenze (9050_CR11) 1994; 7 DE Rumelhart (9050_CR1) 1986 HJ Kushner (9050_CR5) 1995; 40 B Lenze (9050_CR3) 2004; 61 DP Bertsekas (9050_CR4) 1996 W Wu (9050_CR7) 2002; 17 Y Yuan (9050_CR13) 2001 M Heywood (9050_CR12) 1995; 6 R Durbin (9050_CR10) 1989; 1 W Wu (9050_CR9) 2005; 16 9050_CR14 YC Liang (9050_CR8) 2002; 42 |
| References_xml | – volume: 40 start-page: 1403 year: 1995 ident: 9050_CR5 publication-title: IEEE Transac Automat Control doi: 10.1109/9.402231 – volume: 16 start-page: 533 year: 2005 ident: 9050_CR9 publication-title: IEEE Transac Neural Networks doi: 10.1109/TNN.2005.844903 – volume-title: Parallel distributed processing, explorations in the microstructure of cognition year: 1986 ident: 9050_CR1 doi: 10.7551/mitpress/5236.001.0001 – volume: 23 start-page: 111 year: 1995 ident: 9050_CR2 publication-title: J South China Univ Techn – volume-title: Optimization theory and methods year: 2001 ident: 9050_CR13 – volume: 1 start-page: 133 year: 1989 ident: 9050_CR10 publication-title: Neural Comput doi: 10.1162/neco.1989.1.1.133 – volume: 7 start-page: 1285 year: 1994 ident: 9050_CR11 publication-title: Neural Networks doi: 10.1016/0893-6080(94)90009-4 – volume: 42 start-page: 311 year: 2002 ident: 9050_CR8 publication-title: Neurocomputing doi: 10.1016/S0925-2312(01)00576-8 – volume: 2 start-page: 627 year: 2004 ident: 9050_CR6 publication-title: Proceed Int Symposium Comput Inform – volume: 61 start-page: 471 year: 2004 ident: 9050_CR3 publication-title: Neurocomputing doi: 10.1016/j.neucom.2004.05.004 – volume: 17 start-page: 331 year: 2002 ident: 9050_CR7 publication-title: Adv Computat Math doi: 10.1023/A:1016249727555 – volume-title: Neuro-dynamic programming year: 1996 ident: 9050_CR4 – ident: 9050_CR14 doi: 10.1109/ICNNB.2005.1614626 – volume: 6 start-page: 893 year: 1995 ident: 9050_CR12 publication-title: IEEE Transac Neural Networks doi: 10.1109/72.392251 |
| SSID | ssj0010020 |
| Score | 1.8113748 |
| Snippet | Sigma-Pi (Σ-Π) neural networks (SPNNs) are known to provide more powerful mapping capability than traditional feed-forward neural networks. A unified... |
| SourceID | proquest pascalfrancis crossref |
| SourceType | Aggregation Database Index Database Enrichment Source |
| StartPage | 177 |
| SubjectTerms | Algorithms Applied sciences Artificial intelligence Computer science; control theory; systems Connectionism. Neural networks Convergence Error functions Exact sciences and technology Machine learning Neural networks |
| Title | Convergence Analysis of Batch Gradient Algorithm for Three Classes of Sigma-Pi Neural Networks |
| URI | https://www.proquest.com/docview/2918338282 |
| Volume | 26 |
| WOSCitedRecordID | wos000250407900003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1573-773X dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0010020 issn: 1370-4621 databaseCode: P5Z dateStart: 19970201 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1573-773X dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0010020 issn: 1370-4621 databaseCode: K7- dateStart: 19970201 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1573-773X dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0010020 issn: 1370-4621 databaseCode: BENPR dateStart: 19970201 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1573-773X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0010020 issn: 1370-4621 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NS8MwFA86PQjitzg_Rg6ehGDSNO1ykk38AGEMnTI8WNIm0YFuc63-_b5krWMIu3gppU1IyHt5X3n5PYROI26ltk0DW9wa4hDliFKUErAsUsFjIaVKfbGJuNNp9vuyWwbc8jKtspKJXlDrUeZi5OeBBObj4B8EF-NP4qpGudPVsoTGMlphQcAcn9_F5PcUwdlC3uGKKQmjgFWnmv7qHPhCnLhAnaSCEjqnl9bHKoclstPaFn_EtNc915v_nfUW2iitTtyassk2WjLDHbRZVXTA5QbfRS-XLgnd38c0uMIrwSOL2yCx3_DNxCeIFbj1_gqjFG8fGGxe3AN-MNiX1zS-9cPg9UOR7gA76A8YtzPNNc_30OP1Ve_ylpQVGEjGI1kQsB7SSEdWW-pw2EJmbdBMBWh9zaVqah6Bv2FDwVSa2owzQ41iqQEvSoGZmFK-j2rD0dAcIBwwLVUQRjq2PJRZ6IABTSTgExiAWog6otX6J1kJT-6qZLwnM2BlR7LEvTqSJbSOzn67jKfYHIsaN-aIOushQXuzECZwXJEwKfdxnszod7j49xFa81Ffn-hyjGrF5MucoNXsuxjkkwZaaV91uvcNz57w7IpneN4_PP0A5Vnqzg |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LT9wwEB7xkoqECrQgoAv1AS6VLJw4Lx-qakuhoIUVUrcSJ4IT27AS7C6bQMWf4jd27CSsEBI3DtyixHk4_uz5xh5_A7AdcSOUSTR2caOpVZSjUjJGkVlkIY9DIWTmkk3E3W5ydiZOp-Cx2QtjwyqbMdEN1GqY2znyXV8g-Dj6B_6P0S21WaPs6mqTQqOCRUc__EOXrfh-9Avbd8f3D_Z7e4e0zipAcx6JkqJFzCIVGWWY1RYLPGP8JAvRkikuZKJ4hBzaBKEns8zk3NNMSy_T6BlIpD4Z4_jcaZgNeBJbrf5OTJ9WLSz3cg5ezGgQ-V6ziuq26qHvxamdGBQsZJQ9s4MLI1lgk5gql8YLs-Bs3cHie_tLS_CxZtWkXXWDZZjSg0-w2GSsIPUA9hnO92yQvdtvqkmjx0KGhvxEi3RFfo9dAFxJ2teXWKvy6oYgpyc9xLsmLn2odqX_9C9vJD3tEyttgu_tVrH0xQr8fZNarsLMYDjQa0B8TwnpB5GKDQ9EHljhQx2FeAoJrgrDdWBNe6d5Lb9us4BcpxPhaAuR1B5aiKRsHb493TKqtEdeK7z1DESTOwSyEy_AD2g1kEnrcapIJ3jZeP3yV_hw2Ds5To-Pup0vMO9muF1QTwtmyvGd3oS5_L7sF-Mt1yUIXLw1uv4DlN9D1A |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Convergence+analysis+of+batch+gradient+algorithm+for+three+classes+of+sigma-pi+neural+networks&rft.jtitle=Neural+processing+letters&rft.au=CHAO+ZHANG&rft.au=WEI+WU&rft.au=YAN+XIONG&rft.date=2007-12-01&rft.pub=Springer&rft.issn=1370-4621&rft.volume=26&rft.issue=3&rft.spage=177&rft.epage=189&rft_id=info:doi/10.1007%2Fs11063-007-9050-0&rft.externalDBID=n%2Fa&rft.externalDocID=19212145 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1370-4621&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1370-4621&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1370-4621&client=summon |