Learning Algorithms for Quaternion-Valued Neural Networks
This paper presents the deduction of the enhanced gradient descent, conjugate gradient, scaled conjugate gradient, quasi-Newton, and Levenberg–Marquardt methods for training quaternion-valued feedforward neural networks, using the framework of the HR calculus. The performances of these algorithms in...
Uložené v:
| Vydané v: | Neural processing letters Ročník 47; číslo 3; s. 949 - 973 |
|---|---|
| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
01.06.2018
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 | This paper presents the deduction of the enhanced gradient descent, conjugate gradient, scaled conjugate gradient, quasi-Newton, and Levenberg–Marquardt methods for training quaternion-valued feedforward neural networks, using the framework of the HR calculus. The performances of these algorithms in the real- and complex-valued cases led to the idea of extending them to the quaternion domain, also. Experiments done using the proposed training methods on time series prediction applications showed a significant performance improvement over the quaternion gradient descent algorithm. |
|---|---|
| AbstractList | This paper presents the deduction of the enhanced gradient descent, conjugate gradient, scaled conjugate gradient, quasi-Newton, and Levenberg–Marquardt methods for training quaternion-valued feedforward neural networks, using the framework of the HR calculus. The performances of these algorithms in the real- and complex-valued cases led to the idea of extending them to the quaternion domain, also. Experiments done using the proposed training methods on time series prediction applications showed a significant performance improvement over the quaternion gradient descent algorithm. |
| Author | Popa, Călin-Adrian |
| Author_xml | – sequence: 1 givenname: Călin-Adrian orcidid: 0000-0003-4445-8091 surname: Popa fullname: Popa, Călin-Adrian email: calin.popa@cs.upt.ro organization: Department of Computer and Software Engineering, Polytechnic University Timişoara |
| BookMark | eNp9kF1LwzAUhoNMcJv-AO8KXkdzmrZJLsfwC4YiqHgX0iSdnV0zkxTx35tRQRD06j1w3ud8vDM06V1vEToFcg6EsIsAQCqKCTAsGFQYDtAUSkYxY_RlkmrKCC6qHI7QLIQNIYnKyRSJlVW-b_t1tujWzrfxdRuyxvnsYVDRpo7r8bPqBmuyOzt41SWJH86_hWN02Kgu2JNvnaOnq8vH5Q1e3V_fLhcrrCnPI9aMNkAp0Y0xmitR1wClqQpCNedGcSosrXVTcQJ1WYMurRKU6aoShhcGNJ2js3Huzrv3wYYoN27wfVopcwGcFkCYSC4YXdq7ELxt5M63W-U_JRC5T0iOCcmUkNwnJCEx7Bej26hiejl61Xb_kvlIhrSlX1v_c9Pf0BfGA3wE |
| CitedBy_id | crossref_primary_10_1007_s10489_022_03849_x crossref_primary_10_1007_s11571_021_09763_1 crossref_primary_10_1016_j_neucom_2021_03_133 crossref_primary_10_1007_s40747_022_00911_6 crossref_primary_10_1109_TNNLS_2020_2979682 crossref_primary_10_1109_ACCESS_2022_3222372 crossref_primary_10_1007_s11831_023_09925_w crossref_primary_10_1007_s10462_019_09752_1 crossref_primary_10_1016_j_apnum_2023_08_006 crossref_primary_10_3390_machines10050333 crossref_primary_10_1080_00207721_2022_2145859 crossref_primary_10_1016_j_neucom_2019_03_026 crossref_primary_10_1007_s11063_018_9948_8 |
| Cites_doi | 10.1109/TSP.2005.845462 10.1016/S0893-6080(05)80056-5 10.1162/neco.1992.4.2.141 10.1109/72.329697 10.1016/0893-6080(88)90003-2 10.1142/S0129065708001403 10.1007/BF01593790 10.1109/TSP.2008.2010600 10.1007/978-3-319-59153-7_32 10.1016/j.renene.2010.12.013 10.1137/0111030 10.1007/978-3-642-24955-6_66 10.1142/S0129065791000261 10.1090/S0025-5718-1970-0274029-X 10.1007/978-3-540-45226-3_44 10.1093/comjnl/7.2.149 10.1002/047084535X 10.1109/TNN.2011.2157358 10.1162/0899766042321779 10.6028/jres.049.044 10.1016/j.neunet.2009.10.006 10.1051/m2an/196903R100351 10.1016/0893-6080(90)90006-7 10.1016/S0893-6080(96)00048-2 10.1093/comjnl/6.2.163 10.1109/TNNLS.2015.2440473 10.1049/ip-g-2.1992.0050 10.1109/TSP.2010.2047719 10.1109/TSP.2010.2048323 10.1109/TNN.2007.895828 10.1016/j.neunet.2007.09.015 10.1109/TNNLS.2014.2320715 10.1109/TNN.2010.2085444 10.1109/72.125864 10.1016/0920-5489(94)90017-5 10.1109/IJCNN.2015.7280450 10.1007/978-0-387-74503-9 10.1109/IJCNN.2011.6033585 10.1109/IJCNN.2010.5596629 10.1007/b105056 10.1007/978-3-319-62524-9_5 10.1109/ICNN.1993.298623 10.1109/ICSMC.1995.538035 10.1109/ICASSP.2012.6288329 10.1007/978-3-319-19824-8_18 10.1109/IJCNN.2010.5596690 10.1007/BFb0047683 10.1007/978-3-319-46675-0_27 10.1109/SYNASC.2016.050 10.1093/oso/9780198538493.001.0001 10.1109/SYNASC.2014.44 10.1109/ICASSP.2009.4960282 10.1007/978-0-387-40065-5 10.1007/978-3-319-26535-3_47 10.1007/978-3-319-58088-3_17 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media, LLC 2017 Copyright Springer Nature B.V. Jun 2018 |
| Copyright_xml | – notice: Springer Science+Business Media, LLC 2017 – notice: Copyright Springer Nature B.V. Jun 2018 |
| DBID | AAYXX CITATION 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/s11063-017-9716-1 |
| DatabaseName | CrossRef ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials 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 One Academic ProQuest One Academic (New) 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 |
| EISSN | 1573-773X |
| EndPage | 973 |
| ExternalDocumentID | 10_1007_s11063_017_9716_1 |
| GroupedDBID | -4Z -5F -5G -BR -EM -Y2 -~C .86 .DC .VR 06D 0R~ 0VY 123 1N0 1SB 2.D 203 28- 29N 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 53G 5QI 5VS 67Z 6NX 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AAHNG AAIAL AAJKR AAJSJ AAKKN AANZL AAOBN AARHV AARTL AATVU AAUYE AAWCG AAYIU AAYOK AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABEEZ ABFTD ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMOR ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACACY ACBXY ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACSNA ACULB ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFGXO AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BENPR BGLVJ BGNMA C24 C6C CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 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 KOW LAK LLZTM M4Y MA- N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9O PF0 PSYQQ PT5 QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SDH SDM SHX SISQX SNE SNPRN SNX SOHCF SOJ SPH SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7R Z7X Z81 Z83 Z88 Z8M Z8R Z8U Z8W Z92 ZMTXR ~EX 77I AASML AAYXX ABDBE ABFSG ACSTC ADHKG AEZWR AFFHD AFHIU AGQPQ AHPBZ AHWEU AIXLP AYFIA CITATION PHGZM PHGZT PQGLB 8FE 8FG AZQEC DWQXO GNUQQ JQ2 P62 PKEHL PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c382t-c73f1330cfddc8a9bb115d6403c88da839e3bcf6801b5b1c5ea937c669d84d1c3 |
| IEDL.DBID | K7- |
| ISICitedReferencesCount | 20 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000434268000014&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 22:46:40 EDT 2025 Sat Nov 29 02:27:47 EST 2025 Tue Nov 18 22:05:16 EST 2025 Fri Feb 21 02:36:42 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Quaternion-valued neural networks Resilient backpropagation SuperSAB Levenberg–Marquardt algorithm Conjugate gradient algorithms Quickprop Scaled conjugate gradient algorithm Time series prediction Quasi-Newton algorithms Delta-bar-delta |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c382t-c73f1330cfddc8a9bb115d6403c88da839e3bcf6801b5b1c5ea937c669d84d1c3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0003-4445-8091 |
| PQID | 2918341079 |
| PQPubID | 2043838 |
| PageCount | 25 |
| ParticipantIDs | proquest_journals_2918341079 crossref_primary_10_1007_s11063_017_9716_1 crossref_citationtrail_10_1007_s11063_017_9716_1 springer_journals_10_1007_s11063_017_9716_1 |
| PublicationCentury | 2000 |
| PublicationDate | 2018-06-01 |
| PublicationDateYYYYMMDD | 2018-06-01 |
| PublicationDate_xml | – month: 06 year: 2018 text: 2018-06-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York – name: Dordrecht |
| PublicationTitle | Neural processing letters |
| PublicationTitleAbbrev | Neural Process Lett |
| PublicationYear | 2018 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Goh, Mandic (CR19) 2007; 20 Took, Mandic (CR51) 2010; 58 CR38 Charalambous (CR11) 1992; 139 CR36 CR34 Xia, Jahanchahi, Mandic (CR57) 2015; 26 Xu, Xia, Mandic (CR59) 2016; 27 Che Ujang, Took, Mandic (CR12) 2010; 23 Arena, Fortuna, Muscato, Xibilia (CR3) 1997; 10 Mandic, Chambers (CR29) 2001 CR2 Xia, Jelfs, Van Hulle, Principe, Mandic (CR58) 2011; 22 Goh, Mandic (CR18) 2005; 53 CR4 Bishop (CR8) 1995 Fletcher, Powell (CR16) 1963; 6 Tollenaere (CR48) 1990; 3 Reeves, Fletcher (CR44) 1964; 7 Goh, Mandic (CR20) 2007; 18 CR46 Hestenes, Stiefel (CR22) 1952; 49 CR42 CR40 Jacobs (CR24) 1988; 1 Battiti (CR6) 1992; 4 Hagan, Menhaj (CR21) 1994; 5 Popa (CR35) 2015; 2015 Amin, Amin, Al-Nuaimi, Murase, Lu, Zhang, Kwok (CR1) 2011 CR15 CR14 Marquardt (CR30) 1963; 11 Popa (CR41) 2017; 2017 CR56 CR55 CR10 CR53 CR52 Nocedal, Wright (CR32) 1999 Polak, Ribiere (CR33) 1969; 3 Barnard (CR5) 1992; 3 Shanno (CR47) 1970; 24 Took, Strbac, Aihara, Mandic (CR54) 2011; 36 Che Ujang, Took, Mandic (CR13) 2011; 22 Luenberger, Ye (CR28) 2008 Popa, Matoušek (CR37) 2015 Beale, Lootsma (CR7) 1972 Took, Mandic (CR49) 2009; 57 Goh, Mandic (CR17) 2004; 16 Zhang (CR60) 2005 Riedmiller (CR45) 1994; 16 CR27 Møller (CR31) 1993; 6 Took, Mandic (CR50) 2010; 58 CR25 Popa (CR39) 2016; 2016 Powell (CR43) 1977; 12 Johansson, Dowla, Goodman (CR26) 1991; 2 Buchholz, Le Bihan (CR9) 2008; 18 Isokawa, Kusakabe, Matsui, Peper, Palade, Howlett, Jai (CR23) 2003 (9716_CR60) 2005 9716_CR46 9716_CR42 D Xu (9716_CR59) 2016; 27 9716_CR40 S Goh (9716_CR18) 2005; 53 C Charalambous (9716_CR11) 1992; 139 M Møller (9716_CR31) 1993; 6 CA Popa (9716_CR37) 2015 B Che Ujang (9716_CR13) 2011; 22 M Powell (9716_CR43) 1977; 12 9716_CR36 E Johansson (9716_CR26) 1991; 2 9716_CR34 E Polak (9716_CR33) 1969; 3 T Isokawa (9716_CR23) 2003 Y Xia (9716_CR57) 2015; 26 S Goh (9716_CR20) 2007; 18 C Bishop (9716_CR8) 1995 R Jacobs (9716_CR24) 1988; 1 9716_CR38 J Nocedal (9716_CR32) 1999 M Riedmiller (9716_CR45) 1994; 16 C Took (9716_CR51) 2010; 58 9716_CR25 M Amin (9716_CR1) 2011 R Battiti (9716_CR6) 1992; 4 D Marquardt (9716_CR30) 1963; 11 M Hestenes (9716_CR22) 1952; 49 Y Xia (9716_CR58) 2011; 22 E Beale (9716_CR7) 1972 S Buchholz (9716_CR9) 2008; 18 CA Popa (9716_CR35) 2015; 2015 CA Popa (9716_CR41) 2017; 2017 P Arena (9716_CR3) 1997; 10 C Took (9716_CR50) 2010; 58 B Che Ujang (9716_CR12) 2010; 23 M Hagan (9716_CR21) 1994; 5 9716_CR27 9716_CR14 D Mandic (9716_CR29) 2001 9716_CR15 9716_CR56 9716_CR10 9716_CR55 9716_CR52 9716_CR53 CA Popa (9716_CR39) 2016; 2016 C Took (9716_CR49) 2009; 57 S Goh (9716_CR19) 2007; 20 E Barnard (9716_CR5) 1992; 3 D Luenberger (9716_CR28) 2008 9716_CR4 R Fletcher (9716_CR16) 1963; 6 T Tollenaere (9716_CR48) 1990; 3 9716_CR2 D Shanno (9716_CR47) 1970; 24 S Goh (9716_CR17) 2004; 16 C Reeves (9716_CR44) 1964; 7 C Took (9716_CR54) 2011; 36 |
| References_xml | – volume: 53 start-page: 1827 issue: 5 year: 2005 end-page: 1836 ident: CR18 article-title: Nonlinear adaptive prediction of complex-valued signals by complex-valued PRNN publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2005.845462 – volume: 6 start-page: 525 issue: 4 year: 1993 end-page: 533 ident: CR31 article-title: A scaled conjugate gradient algorithm for fast supervised learning publication-title: Neural Netw doi: 10.1016/S0893-6080(05)80056-5 – volume: 4 start-page: 141 issue: 2 year: 1992 end-page: 166 ident: CR6 article-title: First and second-order methods for learning between steepest descent and Newton’s method publication-title: Neural Comput doi: 10.1162/neco.1992.4.2.141 – volume: 5 start-page: 989 issue: 6 year: 1994 end-page: 993 ident: CR21 article-title: Training feedforward networks with the Marquardt algorithm publication-title: IEEE Trans Neural Netw doi: 10.1109/72.329697 – year: 2005 ident: CR60 publication-title: The Schur complement and its applications – ident: CR4 – volume: 1 start-page: 295 issue: 4 year: 1988 end-page: 307 ident: CR24 article-title: Increased rates of convergence through learning rate adaptation publication-title: Neural Netw doi: 10.1016/0893-6080(88)90003-2 – volume: 18 start-page: 75 issue: 2 year: 2008 end-page: 85 ident: CR9 article-title: Polarized signal classification by complex and quaternionic multi-layer perceptrons publication-title: Int J Neural Syst doi: 10.1142/S0129065708001403 – volume: 12 start-page: 241 issue: 1 year: 1977 end-page: 254 ident: CR43 article-title: Restart procedures for the conjugate gradient method publication-title: Math Program doi: 10.1007/BF01593790 – volume: 57 start-page: 1316 issue: 4 year: 2009 end-page: 1327 ident: CR49 article-title: The quaternion LMS algorithm for adaptive filtering of hypercomplex processes publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2008.2010600 – volume: 2017 start-page: 362 year: 2017 end-page: 374 ident: CR41 article-title: Quasi-newton learning methods for quaternion-valued neural networks publication-title: Adv Comput Intell IWANN doi: 10.1007/978-3-319-59153-7_32 – ident: CR25 – ident: CR42 – volume: 36 start-page: 1754 issue: 6 year: 2011 end-page: 1760 ident: CR54 article-title: Quaternion-valued short-term joint forecasting of three-dimensional wind and atmospheric parameters publication-title: Renew Energy doi: 10.1016/j.renene.2010.12.013 – ident: CR46 – volume: 11 start-page: 431 issue: 2 year: 1963 end-page: 441 ident: CR30 article-title: An algorithm for least-squares estimation of nonlinear parameters publication-title: J Soc Ind Appl Math doi: 10.1137/0111030 – start-page: 550 year: 2011 end-page: 559 ident: CR1 article-title: Wirtinger calculus based gradient descent and Levenberg–Marquardt learning algorithms in complex-valued neural networks publication-title: Neural information processing. Lecture notes in computer science doi: 10.1007/978-3-642-24955-6_66 – ident: CR15 – volume: 2 start-page: 291 issue: 4 year: 1991 end-page: 301 ident: CR26 article-title: Backpropagation learning for multilayer feed-forward neural networks using the conjugate gradient method publication-title: Int J Neural Syst doi: 10.1142/S0129065791000261 – volume: 24 start-page: 647 issue: 111 year: 1970 end-page: 656 ident: CR47 article-title: Conditioning of quasi-Newton methods for function minimization publication-title: Math Comput doi: 10.1090/S0025-5718-1970-0274029-X – start-page: 318 year: 2003 end-page: 324 ident: CR23 article-title: Quaternion neural network and its application publication-title: Knowledge-based intelligent information and engineering systems. Lecture notes in computer science doi: 10.1007/978-3-540-45226-3_44 – ident: CR36 – volume: 7 start-page: 149 issue: 2 year: 1964 end-page: 154 ident: CR44 article-title: Function minimization by conjugate gradients publication-title: Comput J doi: 10.1093/comjnl/7.2.149 – year: 2001 ident: CR29 publication-title: Recurrent neural networks for prediction: learning algorithms, architectures and stability doi: 10.1002/047084535X – year: 2008 ident: CR28 publication-title: Linear and nonlinear programming. International series in operations research & management science – volume: 22 start-page: 1193 issue: 8 year: 2011 end-page: 1206 ident: CR13 article-title: Quaternion-valued nonlinear adaptive filtering publication-title: IEEE Trans Neural Netw doi: 10.1109/TNN.2011.2157358 – volume: 16 start-page: 2699 issue: 12 year: 2004 end-page: 2713 ident: CR17 article-title: A complex-valued RTRL algorithm for recurrent neural networks publication-title: Neural Comput doi: 10.1162/0899766042321779 – volume: 49 start-page: 409 issue: 6 year: 1952 end-page: 436 ident: CR22 article-title: Methods of conjugate gradients for solving linear systems publication-title: J Res Natl Bur Stand doi: 10.6028/jres.049.044 – ident: CR14 – ident: CR2 – ident: CR53 – volume: 23 start-page: 426 issue: 3 year: 2010 end-page: 434 ident: CR12 article-title: Split quaternion nonlinear adaptive filtering publication-title: Neural Netw doi: 10.1016/j.neunet.2009.10.006 – volume: 3 start-page: 35 issue: 16 year: 1969 end-page: 43 ident: CR33 article-title: Note sur la convergence de méthodes de directions conjuguées publication-title: Revue Française d’Informatique et de Recherche Opérationnelle doi: 10.1051/m2an/196903R100351 – ident: CR10 – volume: 3 start-page: 561 issue: 5 year: 1990 end-page: 573 ident: CR48 article-title: Supersab: fast adaptive back propagation with good scaling properties publication-title: Neural Netw doi: 10.1016/0893-6080(90)90006-7 – volume: 10 start-page: 335 issue: 2 year: 1997 end-page: 342 ident: CR3 article-title: Multilayer perceptrons to approximate quaternion valued functions publication-title: Neural Netw doi: 10.1016/S0893-6080(96)00048-2 – volume: 6 start-page: 163 issue: 2 year: 1963 end-page: 168 ident: CR16 article-title: A rapidly convergent descent method for minimization publication-title: Comput J doi: 10.1093/comjnl/6.2.163 – ident: CR56 – volume: 2016 start-page: 243 year: 2016 end-page: 252 ident: CR39 article-title: Scaled conjugate gradient learning for quaternion-valued neural networks publication-title: Neural Inf Process ICONIP – ident: CR40 – volume: 27 start-page: 249 issue: 2 year: 2016 end-page: 261 ident: CR59 article-title: Optimization in quaternion dynamic systems: gradient, Hessian, and learning algorithms publication-title: IEEE Trans Neural Netw Learn Syst doi: 10.1109/TNNLS.2015.2440473 – ident: CR27 – volume: 139 start-page: 301 issue: 3 year: 1992 end-page: 310 ident: CR11 article-title: Conjugate gradient algorithm for efficient training of artificial neural networks publication-title: IEE Proc G Circuits Devices Syst doi: 10.1049/ip-g-2.1992.0050 – volume: 58 start-page: 3895 issue: 7 year: 2010 end-page: 3901 ident: CR50 article-title: Quaternion-valued stochastic gradient-based adaptive IIR filtering publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2010.2047719 – year: 1995 ident: CR8 publication-title: Neural networks for pattern recognition – volume: 58 start-page: 4427 issue: 8 year: 2010 end-page: 4431 ident: CR51 article-title: A quaternion widely linear adaptive filter publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2010.2048323 – volume: 18 start-page: 1511 issue: 5 year: 2007 end-page: 1516 ident: CR20 article-title: Stochastic gradient-adaptive complex-valued nonlinear neural adaptive filters with a gradient-adaptive step size publication-title: IEEE Trans Neural Netw doi: 10.1109/TNN.2007.895828 – start-page: 39 year: 1972 end-page: 43 ident: CR7 article-title: A derivation of conjugate gradients publication-title: Numerical methods for nonlinear optimization – start-page: 221 year: 2015 end-page: 233 ident: CR37 article-title: Scaled conjugate gradient learning for complex-valued neural networks publication-title: Mendel 2015. Advances in intelligent systems and computing – ident: CR38 – ident: CR52 – volume: 20 start-page: 1061 issue: 10 year: 2007 end-page: 1066 ident: CR19 article-title: An augmented CRTRL for complex-valued recurrent neural networks publication-title: Neural Netw doi: 10.1016/j.neunet.2007.09.015 – volume: 26 start-page: 663 issue: 4 year: 2015 end-page: 673 ident: CR57 article-title: Quaternion-valued echo state networks publication-title: IEEE Trans Neural Netw Learn Syst doi: 10.1109/TNNLS.2014.2320715 – volume: 22 start-page: 74 issue: 1 year: 2011 end-page: 83 ident: CR58 article-title: An augmented echo state network for nonlinear adaptive filtering of complex noncircular signals publication-title: IEEE Trans Neural Netw doi: 10.1109/TNN.2010.2085444 – volume: 3 start-page: 232 issue: 2 year: 1992 end-page: 240 ident: CR5 article-title: Optimization for training neural nets publication-title: IEEE Trans Neural Netw doi: 10.1109/72.125864 – ident: CR34 – volume: 16 start-page: 265 issue: 3 year: 1994 end-page: 278 ident: CR45 article-title: Advanced supervised learning in multi-layer perceptrons—from backpropagation to adaptive learning algorithms publication-title: Comput Stand Interfaces doi: 10.1016/0920-5489(94)90017-5 – ident: CR55 – year: 1999 ident: CR32 publication-title: Numerical optimization. Springer series in operations research – volume: 2015 start-page: 412 year: 2015 end-page: 422 ident: CR35 article-title: Conjugate gradient algorithms for complex-valued neural networks publication-title: Neural Inf Process ICONIP – volume: 1 start-page: 295 issue: 4 year: 1988 ident: 9716_CR24 publication-title: Neural Netw doi: 10.1016/0893-6080(88)90003-2 – volume: 10 start-page: 335 issue: 2 year: 1997 ident: 9716_CR3 publication-title: Neural Netw doi: 10.1016/S0893-6080(96)00048-2 – ident: 9716_CR36 doi: 10.1109/IJCNN.2015.7280450 – volume: 5 start-page: 989 issue: 6 year: 1994 ident: 9716_CR21 publication-title: IEEE Trans Neural Netw doi: 10.1109/72.329697 – volume: 20 start-page: 1061 issue: 10 year: 2007 ident: 9716_CR19 publication-title: Neural Netw doi: 10.1016/j.neunet.2007.09.015 – volume: 36 start-page: 1754 issue: 6 year: 2011 ident: 9716_CR54 publication-title: Renew Energy doi: 10.1016/j.renene.2010.12.013 – volume-title: Linear and nonlinear programming. International series in operations research & management science year: 2008 ident: 9716_CR28 doi: 10.1007/978-0-387-74503-9 – start-page: 318 volume-title: Knowledge-based intelligent information and engineering systems. Lecture notes in computer science year: 2003 ident: 9716_CR23 doi: 10.1007/978-3-540-45226-3_44 – ident: 9716_CR55 doi: 10.1109/IJCNN.2011.6033585 – ident: 9716_CR25 doi: 10.1109/IJCNN.2010.5596629 – volume: 27 start-page: 249 issue: 2 year: 2016 ident: 9716_CR59 publication-title: IEEE Trans Neural Netw Learn Syst doi: 10.1109/TNNLS.2015.2440473 – start-page: 550 volume-title: Neural information processing. Lecture notes in computer science year: 2011 ident: 9716_CR1 doi: 10.1007/978-3-642-24955-6_66 – volume: 11 start-page: 431 issue: 2 year: 1963 ident: 9716_CR30 publication-title: J Soc Ind Appl Math doi: 10.1137/0111030 – volume: 3 start-page: 35 issue: 16 year: 1969 ident: 9716_CR33 publication-title: Revue Française d’Informatique et de Recherche Opérationnelle doi: 10.1051/m2an/196903R100351 – volume-title: The Schur complement and its applications year: 2005 ident: 9716_CR60 doi: 10.1007/b105056 – volume: 6 start-page: 525 issue: 4 year: 1993 ident: 9716_CR31 publication-title: Neural Netw doi: 10.1016/S0893-6080(05)80056-5 – ident: 9716_CR42 doi: 10.1007/978-3-319-62524-9_5 – ident: 9716_CR46 doi: 10.1109/ICNN.1993.298623 – ident: 9716_CR2 doi: 10.1109/ICSMC.1995.538035 – ident: 9716_CR14 doi: 10.1109/ICASSP.2012.6288329 – volume: 3 start-page: 232 issue: 2 year: 1992 ident: 9716_CR5 publication-title: IEEE Trans Neural Netw doi: 10.1109/72.125864 – volume: 139 start-page: 301 issue: 3 year: 1992 ident: 9716_CR11 publication-title: IEE Proc G Circuits Devices Syst doi: 10.1049/ip-g-2.1992.0050 – volume: 18 start-page: 75 issue: 2 year: 2008 ident: 9716_CR9 publication-title: Int J Neural Syst doi: 10.1142/S0129065708001403 – start-page: 221 volume-title: Mendel 2015. Advances in intelligent systems and computing year: 2015 ident: 9716_CR37 doi: 10.1007/978-3-319-19824-8_18 – volume: 49 start-page: 409 issue: 6 year: 1952 ident: 9716_CR22 publication-title: J Res Natl Bur Stand doi: 10.6028/jres.049.044 – volume: 4 start-page: 141 issue: 2 year: 1992 ident: 9716_CR6 publication-title: Neural Comput doi: 10.1162/neco.1992.4.2.141 – volume: 57 start-page: 1316 issue: 4 year: 2009 ident: 9716_CR49 publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2008.2010600 – ident: 9716_CR52 doi: 10.1109/IJCNN.2010.5596690 – volume: 3 start-page: 561 issue: 5 year: 1990 ident: 9716_CR48 publication-title: Neural Netw doi: 10.1016/0893-6080(90)90006-7 – volume: 53 start-page: 1827 issue: 5 year: 2005 ident: 9716_CR18 publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2005.845462 – ident: 9716_CR4 doi: 10.1007/BFb0047683 – volume: 18 start-page: 1511 issue: 5 year: 2007 ident: 9716_CR20 publication-title: IEEE Trans Neural Netw doi: 10.1109/TNN.2007.895828 – volume: 26 start-page: 663 issue: 4 year: 2015 ident: 9716_CR57 publication-title: IEEE Trans Neural Netw Learn Syst doi: 10.1109/TNNLS.2014.2320715 – volume: 23 start-page: 426 issue: 3 year: 2010 ident: 9716_CR12 publication-title: Neural Netw doi: 10.1016/j.neunet.2009.10.006 – volume: 2017 start-page: 362 year: 2017 ident: 9716_CR41 publication-title: Adv Comput Intell IWANN doi: 10.1007/978-3-319-59153-7_32 – volume: 16 start-page: 265 issue: 3 year: 1994 ident: 9716_CR45 publication-title: Comput Stand Interfaces doi: 10.1016/0920-5489(94)90017-5 – volume: 24 start-page: 647 issue: 111 year: 1970 ident: 9716_CR47 publication-title: Math Comput doi: 10.1090/S0025-5718-1970-0274029-X – ident: 9716_CR27 – volume: 58 start-page: 3895 issue: 7 year: 2010 ident: 9716_CR50 publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2010.2047719 – ident: 9716_CR10 – volume: 2016 start-page: 243 year: 2016 ident: 9716_CR39 publication-title: Neural Inf Process ICONIP doi: 10.1007/978-3-319-46675-0_27 – ident: 9716_CR38 doi: 10.1109/SYNASC.2016.050 – volume-title: Recurrent neural networks for prediction: learning algorithms, architectures and stability year: 2001 ident: 9716_CR29 doi: 10.1002/047084535X – volume: 2 start-page: 291 issue: 4 year: 1991 ident: 9716_CR26 publication-title: Int J Neural Syst doi: 10.1142/S0129065791000261 – volume: 12 start-page: 241 issue: 1 year: 1977 ident: 9716_CR43 publication-title: Math Program doi: 10.1007/BF01593790 – volume-title: Neural networks for pattern recognition year: 1995 ident: 9716_CR8 doi: 10.1093/oso/9780198538493.001.0001 – ident: 9716_CR56 – ident: 9716_CR34 doi: 10.1109/SYNASC.2014.44 – volume: 7 start-page: 149 issue: 2 year: 1964 ident: 9716_CR44 publication-title: Comput J doi: 10.1093/comjnl/7.2.149 – volume: 22 start-page: 74 issue: 1 year: 2011 ident: 9716_CR58 publication-title: IEEE Trans Neural Netw doi: 10.1109/TNN.2010.2085444 – volume: 58 start-page: 4427 issue: 8 year: 2010 ident: 9716_CR51 publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2010.2048323 – ident: 9716_CR53 doi: 10.1109/ICASSP.2009.4960282 – volume: 16 start-page: 2699 issue: 12 year: 2004 ident: 9716_CR17 publication-title: Neural Comput doi: 10.1162/0899766042321779 – volume-title: Numerical optimization. Springer series in operations research year: 1999 ident: 9716_CR32 doi: 10.1007/978-0-387-40065-5 – volume: 2015 start-page: 412 year: 2015 ident: 9716_CR35 publication-title: Neural Inf Process ICONIP doi: 10.1007/978-3-319-26535-3_47 – ident: 9716_CR40 doi: 10.1007/978-3-319-58088-3_17 – ident: 9716_CR15 – volume: 6 start-page: 163 issue: 2 year: 1963 ident: 9716_CR16 publication-title: Comput J doi: 10.1093/comjnl/6.2.163 – start-page: 39 volume-title: Numerical methods for nonlinear optimization year: 1972 ident: 9716_CR7 – volume: 22 start-page: 1193 issue: 8 year: 2011 ident: 9716_CR13 publication-title: IEEE Trans Neural Netw doi: 10.1109/TNN.2011.2157358 |
| SSID | ssj0010020 |
| Score | 2.2553608 |
| Snippet | This paper presents the deduction of the enhanced gradient descent, conjugate gradient, scaled conjugate gradient, quasi-Newton, and Levenberg–Marquardt... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 949 |
| SubjectTerms | Algorithms Approximation Artificial Intelligence Artificial neural networks Back propagation Calculus Complex Systems Computational Intelligence Computer Science Conjugate gradient method Machine learning Neural networks Quaternions Teaching methods Time series |
| SummonAdditionalLinks | – databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT8MwDI7Q4MCF8RSDgXrgBIrUrGmbHCfExGniOe1WJU46Jo0NrR2_H6ePVSBAglulpm7lR_y5dmxCLiyLYmYMGhKAppy5K2M0hRCgF6BGM5YWwybi4VCMx_KuOsed1dXudUqy2Kmbw24Yvbjan5i6tkcUQ55N9HbCWePD42idOnAAqIiyYp_yqMfqVOZ3JD47owZhfkmKFr5m0P7XV-6SnQpaev1SF_bIhp3vk3Y9tsGrrPiAyKqn6sTrzyaL5TR_ec08xK7e_Uq534MoKTpSs5U1nmvdgSSHZa14dkieBzdP17e0mqBAIRC9nEIcpBiE-pAaA0JJrREAmoj7AQhhFIIjG2hII3RTOtQMQqsQrkAUSSO4YRAckdZ8MbfHxJNKcK5ZariMuGJWMhMaHvvKd0PMhOwQv2ZlAlV7cTflYpY0jZEdaxJkTeJYk7AOuVw_8lb21vhtcbeWT1KZWZb0JO5IHCNYfP1VLY_m9o_ETv60-pRsI0wSZYFYl7Ty5cqekS14z6fZ8rzQvg8zyNKH priority: 102 providerName: Springer Nature |
| Title | Learning Algorithms for Quaternion-Valued Neural Networks |
| URI | https://link.springer.com/article/10.1007/s11063-017-9716-1 https://www.proquest.com/docview/2918341079 |
| Volume | 47 |
| WOSCitedRecordID | wos000434268000014&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/eLvHCXMwpV1LS8NAEB60evBifWJ9lBw8KYvZZJPsnkSlRRBKrQ_ES0hmkyrUVk3q73c23VgU9OJlCSQZws7s7jePzAdwmPEw4lrTQkJMmeDmSuuUYYDo-WTRnOcV2UTU68mHB9W3AbfCllXWe2K1UesJmhj5iafI-AQ5K-r09Y0Z1iiTXbUUGouwxD2PGzu_ithXFsFgocrhilwmQo_XWc3q1znyhUwlUcRMEyXGv59Lc7D5Iz9aHTvd5n8_eA1WLeB0zmYWsg4L2XgDmjWZg2PX9iYo22l16JyNhiSnfHopHEK0zvU0MUFD0h-7T0bTTDumoQeJ7M0qyIstuOt2bi8umeVVYOhLr2QY-Tm5pi7mWqNMVJoSLNShcH2UUicEmTI_xTykwysNUo5BlhCIwTBUWgrN0d-GxngyznbAUYkUIuW5FioUCc8U14EWkZu4htpMqha49azGaJuOG-6LUTxvl2wUEZMiYqOImLfg6OuV11nHjb8e3q8nP7aLr4jnM9-C41p989u_Ctv9W9gerBBakrM6sX1olO_T7ACW8aN8Lt7bsHTe6fUH7coCaewHjzQObu4_AfXE4JE |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LS8QwEB58gV58i-uzB70owabNtslBRHygrC4KKt5qO0lXYV0f3VX8U_5GJ324KOjNg7dC26HNfJnMZCbzAawZHoRca5pIiAkT3F5pnTCsI3o-IZrzNCebCJtNeX2tzgbgvToLY8sqK5uYG2r9gHaPfMtTBD5BwYraeXxiljXKZlcrCo0CFg3z9kohW7Z9vE_6Xfe8w4OLvSNWsgow9KXXZRj6KQVmLqZao4xVkpBTpAPh-iiljslhMH6CaUCmO6knHOsmpiUcg0BpKTRHn-QOwrDwZWh79TdC9pm1sL5XHuCFLhOBx6ssan5Uj2IvW7kUMtu0ifGv62Dfuf2Wj82XucOJ_zZAkzBeOtTObjEDpmDAdKZhoiKrcErbNQOq7CTbcnbbLfru7u195pDH7pz3YrspSvhkV3G7Z7RjG5aQyGZRIZ_NwuWf_MAcDHUeOmYeHBVLIRKeaqECEXOjuK5rEbqxa6nbpKqBW2kxwrKpuuX2aEf9dtBW8REpPrKKj3gNNj5feSw6ivz28FKl7Kg0LlnU13QNNiu49G__KGzhd2GrMHp0cXoSnRw3G4swRp6hLGrilmCo-9wzyzCCL9277HklR70DN3-Nog-UyTtH |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1dS8MwFA2iIr44P3E6tQ8-KWFNm7XJ41CHopSJOvYWmqSdg9mNtfP3e9OPFUUF8a3QNC03N825uTfnIHQeEc8nWsNEUkpiSsyV1hKrjlKOCx5NSJyLTfhBwIZD3i91TtOq2r1KSRZnGgxLU5K1Zzpu1wffIJIxdUA-NhRIGMKfNWo0g0y4_jRYphEMGMojLt_G1HNIldb8rovPC1ONNr8kSPN1p9f49xdvo60Sclrdwkd20EqU7KJGJedglbN7D_GSa3VkdSej6Xycvb6lFmBa63ERmm1DGEE8CCeLSFuG0gO6DIoa8nQfvfRunq9ucamsgJXLnAwr340hOLVVrLViIZcSgKH2qO0qxnQIoClypYo9WL5kRxLViUKAMcrzuGZUE-UeoNVkmkSHyOIho1SSWFPu0ZBEnOiOpr4d2kbcjPEmsiuzClXSjhv1i4moCZONaQSYRhjTCNJEF8tHZgXnxm-NW9VYiXL6pcLh8KcCh_Dh9ZfV2NS3f-zs6E-tz9BG_7onHu6C-2O0CUiKFTVkLbSazRfRCVpX79k4nZ_mTvkBhz7eTw |
| 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=Learning+Algorithms+for+Quaternion-Valued+Neural+Networks&rft.jtitle=Neural+processing+letters&rft.date=2018-06-01&rft.pub=Springer+Nature+B.V&rft.issn=1370-4621&rft.eissn=1573-773X&rft.volume=47&rft.issue=3&rft.spage=949&rft.epage=973&rft_id=info:doi/10.1007%2Fs11063-017-9716-1 |
| 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 |