A Novel Fractional Gradient-Based Learning Algorithm for Recurrent Neural Networks
In this research, we propose a novel algorithm for learning of the recurrent neural networks called as the fractional back-propagation through time (FBPTT). Considering the potential of the fractional calculus, we propose to use the fractional calculus-based gradient descent method to derive the FBP...
Saved in:
| Published in | Circuits, systems, and signal processing Vol. 37; no. 2; pp. 593 - 612 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.02.2018
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0278-081X 1531-5878 |
| DOI | 10.1007/s00034-017-0572-z |
Cover
| Abstract | In this research, we propose a novel algorithm for learning of the recurrent neural networks called as the fractional back-propagation through time (FBPTT). Considering the potential of the fractional calculus, we propose to use the fractional calculus-based gradient descent method to derive the FBPTT algorithm. The proposed FBPTT method is shown to outperform the conventional back-propagation through time algorithm on three major problems of estimation namely nonlinear system identification, pattern classification and Mackey–Glass chaotic time series prediction. |
|---|---|
| AbstractList | In this research, we propose a novel algorithm for learning of the recurrent neural networks called as the fractional back-propagation through time (FBPTT). Considering the potential of the fractional calculus, we propose to use the fractional calculus-based gradient descent method to derive the FBPTT algorithm. The proposed FBPTT method is shown to outperform the conventional back-propagation through time algorithm on three major problems of estimation namely nonlinear system identification, pattern classification and Mackey–Glass chaotic time series prediction. |
| Author | Khan, Shujaat Ahmad, Jawwad Naseem, Imran Moinuddin, Muhammad |
| Author_xml | – sequence: 1 givenname: Shujaat orcidid: 0000-0001-9676-6817 surname: Khan fullname: Khan, Shujaat organization: Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), Faculty of Engineering Science and Technology, Iqra University – sequence: 2 givenname: Jawwad surname: Ahmad fullname: Ahmad, Jawwad organization: Department of Electrical Engineering, Usman Institute of Technology – sequence: 3 givenname: Imran orcidid: 0000-0003-4429-0049 surname: Naseem fullname: Naseem, Imran email: imran.naseem@uwa.edu.au organization: College of Engineering, Karachi Institute of Economics and Technology, School of Electrical, Electronic and Computer Engineering, The University of Western Australia – sequence: 4 givenname: Muhammad surname: Moinuddin fullname: Moinuddin, Muhammad organization: Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University |
| BookMark | eNp9kE1LxDAQhoMouH78AG8Fz9FJsmna4yp-wbKCKHgLaTpdu9ZGJ13F_fVmWQ8i6GkO8z7z8eyx7T70yNiRgBMBYE4jAKgxB2E4aCP5aouNhFaC68IU22wE0hQcCvG4y_ZiXACIclzKEbubZLPwjl12Sc4Pbehdl12Rq1vsB37mItbZFB31bT_PJt08UDs8vWRNoOwO_ZIoxbIZLilhMxw-Aj3HA7bTuC7i4XfdZw-XF_fn13x6e3VzPplyr0Q-cNlUedloj74sfVGiyrVEzGVVOacrVwsvKpM-SF09BjRjDVIaULXSNYCs1T473sx9pfC2xDjYRVhSeiDaBCmpcyVFSolNylOIkbCxr9S-OPq0Auxand2os0mdXauzq8SYX4xvB7e2M5Bru39JuSFj2tLPkX7c9Cf0BRRahSA |
| CitedBy_id | crossref_primary_10_3390_app12189264 crossref_primary_10_1140_epjs_s11734_022_00455_3 crossref_primary_10_3390_fractalfract7110789 crossref_primary_10_1016_j_rineng_2025_104450 crossref_primary_10_1007_s00521_022_07728_x crossref_primary_10_1007_s10462_023_10474_8 crossref_primary_10_1016_j_jfranklin_2021_12_022 crossref_primary_10_1016_j_jfranklin_2024_01_013 crossref_primary_10_1016_j_chaos_2025_116009 crossref_primary_10_1016_j_isatra_2024_04_019 crossref_primary_10_2478_cait_2020_0041 crossref_primary_10_1088_1742_6596_1969_1_012038 crossref_primary_10_1155_2021_5517502 crossref_primary_10_3390_machines9110247 crossref_primary_10_3390_batteries8100148 crossref_primary_10_3389_fnsys_2024_1269190 crossref_primary_10_1007_s11063_022_10925_3 crossref_primary_10_1016_j_neunet_2021_06_021 crossref_primary_10_1007_s11063_024_11571_7 crossref_primary_10_1155_2022_9755422 crossref_primary_10_3389_fphy_2023_1201053 crossref_primary_10_3390_e25010035 crossref_primary_10_1007_s00034_021_01715_8 crossref_primary_10_1016_j_amc_2020_125797 crossref_primary_10_1016_j_jfranklin_2020_01_008 crossref_primary_10_3390_fractalfract6110640 crossref_primary_10_3390_fractalfract7020132 crossref_primary_10_3390_fractalfract9020091 crossref_primary_10_1007_s10994_023_06314_z |
| Cites_doi | 10.1016/j.ifacol.2016.03.131 10.1109/ICETECH.2015.7275027 10.1162/neco.1990.2.4.490 10.1117/12.668189 10.1109/ICASSP.2016.7472844 10.1109/ICASSP.2016.7472917 10.1109/ICASSP.2014.6854661 10.1007/s00521-016-2548-5 10.1155/2008/369421 10.1109/ICCSCE.2016.7893626 10.1109/LSP.2015.2394301 10.1155/S0161171203301486 10.1007/978-1-4020-6042-7 10.1109/ICASSP.2015.7178896 10.1016/j.aml.2008.06.003 10.1177/1077546307087435 10.1126/science.286.5439.531 10.18653/v1/N16-1037 10.1016/j.neucom.2016.02.017 10.2478/s11534-013-0256-7 10.1088/1674-1056/23/5/050503 10.1109/ICASSP.2013.6639310 10.1016/S0893-6080(05)80125-X 10.1109/ICCV.2015.179 10.1016/j.ifacol.2015.08.048 10.1109/BIGCOMP.2016.7425963 10.23919/ECC.2013.6669201 10.1109/TCST.2010.2042296 10.1109/TNNLS.2013.2271778 10.1016/j.camwa.2006.02.001 10.1177/1077546307087433 10.1109/ICASSP.2016.7472621 10.1177/1077546307087440 10.1109/TNNLS.2014.2344002 10.1002/prot.21078 10.1016/j.automatica.2005.08.017 10.1177/1077546307087439 10.1016/j.sigpro.2005.10.017 10.1016/j.nonrwa.2009.01.003 10.1109/ICASSP.2016.7472841 10.1109/TPAMI.2005.159 10.1109/ICRA.2016.7487174 10.1016/0893-6080(89)90022-1 10.2307/2687575 10.21437/Interspeech.2015-696 10.21437/Interspeech.2015-350 10.1007/s00034-016-0375-7 10.1137/1018042 10.1016/j.conb.2015.07.006 10.1109/TIE.2011.2134057 10.1016/j.sigpro.2014.06.015 10.20965/jaciii.2007.p1079 10.1109/TIE.2016.2542787 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media New York 2017 Circuits, Systems, and Signal Processing is a copyright of Springer, (2017). All Rights Reserved. |
| Copyright_xml | – notice: Springer Science+Business Media New York 2017 – notice: Circuits, Systems, and Signal Processing is a copyright of Springer, (2017). All Rights Reserved. |
| DBID | AAYXX CITATION 3V. 7SC 7SP 7XB 88I 8AL 8AO 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- L6V L7M L~C L~D M0N M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U S0W |
| DOI | 10.1007/s00034-017-0572-z |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Electronics & Communications Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central ProQuest Technology Collection ProQuest One Community College ProQuest Central ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Science Database Engineering 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 ProQuest One Academic UKI Edition ProQuest Central China Engineering collection ProQuest Central Basic DELNET Engineering & Technology Collection |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Pharma Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection ProQuest Computing Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition Electronics & Communications Abstracts ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition ProQuest DELNET Engineering and Technology Collection Materials Science & Engineering Collection ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New) |
| DatabaseTitleList | Computer Science Database |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1531-5878 |
| EndPage | 612 |
| ExternalDocumentID | 10_1007_s00034_017_0572_z |
| GroupedDBID | -5B -5G -BR -EM -Y2 -~C -~X .86 .VR 06D 0R~ 0VY 1N0 1SB 2.D 203 28- 29B 29~ 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 88I 8AO 8FE 8FG 8FW 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHQN ABJCF ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFEXP AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCEE ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. BA0 BBWZM BDATZ BENPR BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CSCUP DDRTE DL5 DNIVK DPUIP DWQXO EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I-F IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X J-C J0Z JBSCW JCJTX JZLTJ K6V K7- KDC KOV KOW L6V LAS LLZTM M0N M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P2P P62 P9P PF0 PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZK S0W S16 S1Z S26 S27 S28 S3B SAP SCLPG SCV SDH SDM SEG SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7R Z7S Z7X Z7Z Z83 Z88 Z8M Z8N Z8R Z8T Z8W Z92 ZMTXR _50 ~A9 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB PUEGO 7SC 7SP 7XB 8AL 8FD 8FK JQ2 L7M L~C L~D PKEHL PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c316t-2fb69f5cec99c89e3652ee62bbaa5bad1c1b753199c540e745022703d35d002d3 |
| IEDL.DBID | BENPR |
| ISSN | 0278-081X |
| IngestDate | Sat Aug 16 06:11:25 EDT 2025 Wed Oct 01 05:53:58 EDT 2025 Thu Apr 24 22:52:13 EDT 2025 Fri Feb 21 02:35:56 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Gradient descent Minimum redundancy and maximum relevance (mRMR) Back-propagation through time (BPTT) Mackey–Glass chaotic time series Fractional calculus Recurrent neural network (RNN) |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c316t-2fb69f5cec99c89e3652ee62bbaa5bad1c1b753199c540e745022703d35d002d3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-9676-6817 0000-0003-4429-0049 |
| PQID | 1993256321 |
| PQPubID | 30136 |
| PageCount | 20 |
| ParticipantIDs | proquest_journals_1993256321 crossref_primary_10_1007_s00034_017_0572_z crossref_citationtrail_10_1007_s00034_017_0572_z springer_journals_10_1007_s00034_017_0572_z |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 20180200 2018-2-00 20180201 |
| PublicationDateYYYYMMDD | 2018-02-01 |
| PublicationDate_xml | – month: 2 year: 2018 text: 20180200 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York – name: Cambridge |
| PublicationSubtitle | CSSP |
| PublicationTitle | Circuits, systems, and signal processing |
| PublicationTitleAbbrev | Circuits Syst Signal Process |
| PublicationYear | 2018 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | H. Sak, A. Senior, K. Rao, F. Beaufays, Fast and accurate recurrent neural network acoustic models for speech recognition. arXiv preprint arXiv:1507.06947 (2015) SunWZhaoYLiJZhangLGaoHActive suspension control with frequency band constraints and actuator input delayIEEE Trans. Ind. Electron.201259153053710.1109/TIE.2011.2134057 TanYHeZTianBA novel generalization of modified lms algorithm to fractional orderIEEE Signal Process. Lett.20152291244124810.1109/LSP.2015.2394301 JumarieGTable of some basic fractional calculus formulae derived from a modified Riemann–Liouville derivative for non-differentiable functionsAppl. Math. Lett.2009223378385248350310.1016/j.aml.2008.06.0031171.26305 A. Joulin, T. Mikolov, Inferring algorithmic patterns with stack-augmented recurrent nets, in Advances in Neural Information Processing Systems 28, eds. by C. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama, R. Garnett (Curran Associates, Inc., 2015), pp. 190–198 S. Zheng, S. Jayasumana, B. Romera-Paredes, V. Vineet, Z. Su, D. Du, C. Huang, P.H. Torr, Conditional random fields as recurrent neural networks, in Proceedings of the IEEE International Conference on Computer Vision, 2015, pp. 1529–1537 M. Zhang, Z. McCarthy, C. Finn, S. Levine, P. Abbeel, Learning deep neural network policies with continuous memory states. arXiv preprint arXiv:1507.01273 (2015) Q.V. Le, N. Jaitly, G.E. Hinton, A simple way to initialize recurrent networks of rectified linear units. arXiv preprint arXiv:1504.00941 (2015) H. Jaeger, Tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and the “echo state network” approach, GMD Report 159, (German National Research Center for Information Technology, 2002), p. 48 GolubTRSlonimDKTamayoPHuardCGaasenbeekMMesirovJPCollerHLohMLDowningJRCaligiuriMAMolecular classification of cancer: class discovery and class prediction by gene expression monitoringScience1999286543953153710.1126/science.286.5439.531 Y. Pu, X. Yuan, K. Liao, J. Zhou, N. Zhang, X. Pu, Y. Zeng, A recursive two-circuits series analog fractance circuit for any order fractional calculus, in ICO20: Optical Information Processing, 60271Y (2006). doi:10.1117/12.668189 R.J. Williams, D. Zipser, Gradient-based learning algorithms for recurrent networks and their computational complexity. Backpropagation Theory Archit. Appl. 1, 433–486 (1995) X. Chen, T. Tan, X. Liu, P. Lanchantin, M. Wan, M.J. Gales, P.C. Woodland, Recurrent neural network language model adaptation for multi-genre broadcast speech recognition, in Proceedings of ISCA Interspeech, Dresden, Germany, 2015, pp. 3511–3515 C. Junhua, D. Baorong, S. Guangren, A novel time-series artificial neural network: a case study for forecasting oil production. Sci. J. Control Eng. 6(1), 1–7 (2016) DoyaKYoshizawaSAdaptive neural oscillator using continuous-time back-propagation learningNeural Netw.19892537538510.1016/0893-6080(89)90022-1 B. Shoaib, I.M. Qureshi, Shafqatullah, Ihsanulhaq, Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction. Chin. Phys. B 23(5), 050503 (2014) JumarieGAn approach via fractional analysis to non-linearity induced by coarse-graining in spaceNonlinear Anal. Real World Appl.2010111535546257057310.1016/j.nonrwa.2009.01.0031195.37054 M. Hermans, M. Soriano, J. Dambre, P. Bienstman, I. Fischer, Photonic delay systems as machine learning implementations. arXiv preprint arXiv:1501.02592 (2015) Y. Ji, G. Haffari, J. Eisenstein, A latent variable recurrent neural network for discourse relation language models. arXiv preprint arXiv:1603.01913 (2016) L. Sun, S. Kang, K. Li, H. Meng, Voice conversion using deep bidirectional long short-term memory based recurrent neural networks, in 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2015, pp. 4869–4873 B. Krishna, K. Reddy, Active and passive realization of fractance device of order 1/2. Active Passive Electron. Compon. 2008, 369421 (2008). doi:10.1155/2008/369421 CerveraJBañosAAutomatic loop shaping in qft using crone structuresJ. Vib. Control2008149–1015131529246296310.1177/10775463070874331229.93069 M. Kleinz, T. Osler, A childs garden of fractional derivatives. The College Math Journal 31(2), 82–88 (2000) J. An, S. Cho, Hand motion identification of grasp-and-lift task from electroencephalography recordings using recurrent neural networks, in 2016 International Conference on Big Data and Smart Computing (BigComp), IEEE, 2016, pp. 427–429 SunWZhangYHuangYGaoHKaynakOTransient-performance-guaranteed robust adaptive control and its application to precision motion control systemsIEEE Trans. Ind. Electron.201663106510651810.1109/TIE.2016.2542787 SunWGaoHKaynakOFinite frequency h∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_{\infty }$$\end{document} control for vehicle active suspension systemsIEEE Trans. Control Syst. Technol.201119241642210.1109/TCST.2010.2042296 P.K. Muthukumar, A.W. Black, Recurrent neural network postfilters for statistical parametric speech synthesis. arXiv preprint arXiv:1601.07215 (2016) W. Zaremba, I. Sutskever, O. Vinyals, Recurrent neural network regularization. arXiv preprint arXiv:1409.2329 (2014) PandaRDashMFractional generalized splines and signal processingSignal Process.20068692340235010.1016/j.sigpro.2005.10.0171172.65315 S. Ravuri, A. Stolcke, Recurrent neural network and lstm models for lexical utterance classification, in Sixteenth Annual Conference of the International Speech Communication Association, 2015 FairbankMAlonsoEProkhorovDAn equivalence between adaptive dynamic programming with a critic and backpropagation through timeIEEE Trans. Neural Netw. Learn. Syst.201324122088210010.1109/TNNLS.2013.2271778 SahaSRaghavaGPrediction of continuous b-cell epitopes in an antigen using recurrent neural networkProteins Struct. Funct. Bioinform.2006651404810.1002/prot.21078 JumarieGModified Riemann–Liouville derivative and fractional taylor series of nondifferentiable functions further resultsComput. Math. Appl.200651913671376223763410.1016/j.camwa.2006.02.0011137.65001 RoudiYTaylorGLearning with hidden variablesCurr. Opin. Neurobiol.20153511011810.1016/j.conb.2015.07.006 DebnathLRecent applications of fractional calculus to science and engineeringInt. J. Math. Math. Sci.200320035434133442202556610.1155/S01611712033014861036.26004 Z. Gan, C. Li, R. Henao, D.E. Carlson, L. Carin, Deep temporal sigmoid belief networks for sequence modeling, in Advances in Neural Information Processing Systems 28, eds. by C. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama, R. Garnett (Curran Associates, Inc., 2015), pp. 2467–2475 SommacalLMelchiorPOustaloupACabelguenJMIjspeertAJFractional multi-models of the frog gastrocnemius muscleJ. Vib. Control2008149–101415143010.1177/10775463070874401229.92019 GeorgeKSubramanianKSheshadhriNImproving transient response in adaptive control of nonlinear systemsIFAC PapersOnLine201649165866310.1016/j.ifacol.2016.03.131 C. Weng, D. Yu, S. Watanabe, B.H.F. Juang, Recurrent deep neural networks for robust speech recognition, in 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2014, pp. 5532–5536 BohannanGWAnalog fractional order controller in temperature and motor control applicationsJ. Vib. Control2008149–1014871498246307410.1177/1077546307087435 WigrenTRecursive prediction error identification and scaling of non-linear state space models using a restricted black box parameterizationAutomatica2006421159168218307810.1016/j.automatica.2005.08.0171121.93316 J. Ahmad, Design of Efficient Adaptive Beamforming Algorithms for Novel Mimo Architectures, Ph.D. Thesis, Iqra University, Karachi (2014) J. Koscak, R. Jaksa, P. Sincák, Prediction of temperature daily profile by stochastic update of backpropagation through time algorithm. J. Math. Syst. Sci. 2(4), 217–225 (2012) BaoGZengZGlobal asymptotical stability analysis for a kind of discrete-time recurrent neural network with discontinuous activation functionsNeurocomputing201619324224910.1016/j.neucom.2016.02.017 N.T. Vu, P. Gupta, H. Adel, H. Schütze, Bi-directional recurrent neural network with ranking loss for spoken language understanding, in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016 LovoieJOslerTJTremblayRFractional derivatives and special functionsSIAM Rev.197618224026840991410.1137/10180420324.44002 W. Chan, N. Jaitly, Q.V. Le, O. Vinyals, Listen, attend and spell: a neural network for large vocabulary conversational speech recognition, in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016 H. Jia, Investigation into the effectiveness of long short term memory networks for stock price prediction. arXiv preprint arXiv:1603.07893 (2016) MaginROvadiaMModeling the cardiac tissue electrode interface using fractional calculusJ. Vib. Control2008149–101431144210.1177/10775463070874391229.92018 A. Mazumder, A. Rakshit, D. Tibarewala, A back-propagation through time based recurrent neural network approach for classification of cognitive eeg states, in 2015 IEEE International Conference on Engineering and Technology (ICETECH), IEEE, 2015, pp. 1–5 HaykinSONeural Networks: A Comprehensive Foundation1994Upper Saddle RiverPrentice Hall PTR0828.68103 WilliamsRJPengJAn efficient gradient-based algorithm for on-line training of recurrent network trajectoriesNeural Comput.19902449050110.1162/neco.1990.2.4.490 J. Amhad, M. Usman, S. Khan, I. Naseem, H.J. Syed, Rvp-flms: a robust variable power fractional lms algorithm, in 2016 IEEE International Conference on Control System, Computing and Engineering (ICCSCE), IEEE, 2016 S. Khan, I. Naseem, R. Togneri, M. Bennamoun, A novel adaptive kernel for the rbf neural networks. Circuits Syst. Signal Process. 36(4), 1639–1653 (2017). doi:10.1007/s00034-016-0375-7 T. 572_CR46 572_CR48 S Saha (572_CR51) 2006; 65 T Wigren (572_CR64) 2006; 42 QV Le (572_CR35) 2015 G Jumarie (572_CR28) 2013; 11 W Sun (572_CR57) 2016; 63 H Peng (572_CR45) 2005; 27 Y Roudi (572_CR49) 2015; 35 SO Haykin (572_CR18) 1994 572_CR52 GW Bohannan (572_CR6) 2008; 14 572_CR10 J Cervera (572_CR7) 2008; 14 572_CR53 572_CR55 572_CR14 MAZ Raja (572_CR47) 2015; 107 572_CR59 EA Antonelo (572_CR4) 2015; 48 R Panda (572_CR43) 2006; 86 G Jumarie (572_CR25) 2006; 51 I Grau (572_CR17) 2013; 17 572_CR61 572_CR63 572_CR62 572_CR21 572_CR65 572_CR20 572_CR23 572_CR67 L Debnath (572_CR11) 2003; 2003 572_CR22 J Sabatier (572_CR50) 2007 G Jumarie (572_CR26) 2009; 22 572_CR69 572_CR24 572_CR68 572_CR1 572_CR3 572_CR29 572_CR2 W Sun (572_CR56) 2011; 19 572_CR9 572_CR8 MF Lima (572_CR37) 2007; 11 K Doya (572_CR12) 1989; 2 TR Golub (572_CR16) 1999; 286 572_CR70 R Magin (572_CR39) 2008; 14 M Fairbank (572_CR13) 2013; 24 572_CR32 572_CR31 572_CR34 572_CR33 572_CR36 F Ken-ichi (572_CR30) 1993; 6 G Jumarie (572_CR27) 2010; 11 L Sommacal (572_CR54) 2008; 14 RJ Williams (572_CR66) 1990; 2 W Sun (572_CR58) 2012; 59 Y Tan (572_CR60) 2015; 22 J Lovoie (572_CR38) 1976; 18 K George (572_CR15) 2016; 49 572_CR41 572_CR40 M Hermans (572_CR19) 2015; 26 572_CR42 G Bao (572_CR5) 2016; 193 572_CR44 |
| References_xml | – reference: H. Jia, Investigation into the effectiveness of long short term memory networks for stock price prediction. arXiv preprint arXiv:1603.07893 (2016) – reference: LimaMFMachadoJATCrisóstomoMMExperimental signal analysis of robot impacts in a fractional calculus perspectiveJACIII20071191079108510.20965/jaciii.2007.p1079 – reference: W. Zaremba, I. Sutskever, O. Vinyals, Recurrent neural network regularization. arXiv preprint arXiv:1409.2329 (2014) – reference: S. Khan, I. Naseem, R. Togneri, M. Bennamoun, A novel adaptive kernel for the rbf neural networks. Circuits Syst. Signal Process. 36(4), 1639–1653 (2017). doi:10.1007/s00034-016-0375-7 – reference: C. Junhua, D. Baorong, S. Guangren, A novel time-series artificial neural network: a case study for forecasting oil production. Sci. J. Control Eng. 6(1), 1–7 (2016) – reference: L. Sun, S. Kang, K. Li, H. Meng, Voice conversion using deep bidirectional long short-term memory based recurrent neural networks, in 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2015, pp. 4869–4873 – reference: X. Chen, T. Tan, X. Liu, P. Lanchantin, M. Wan, M.J. Gales, P.C. Woodland, Recurrent neural network language model adaptation for multi-genre broadcast speech recognition, in Proceedings of ISCA Interspeech, Dresden, Germany, 2015, pp. 3511–3515 – reference: RoudiYTaylorGLearning with hidden variablesCurr. Opin. Neurobiol.20153511011810.1016/j.conb.2015.07.006 – reference: J. Amhad, M. Usman, S. Khan, I. Naseem, H.J. Syed, Rvp-flms: a robust variable power fractional lms algorithm, in 2016 IEEE International Conference on Control System, Computing and Engineering (ICCSCE), IEEE, 2016 – reference: N.T. Vu, P. Gupta, H. Adel, H. Schütze, Bi-directional recurrent neural network with ranking loss for spoken language understanding, in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016 – reference: SunWGaoHKaynakOFinite frequency h∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_{\infty }$$\end{document} control for vehicle active suspension systemsIEEE Trans. Control Syst. Technol.201119241642210.1109/TCST.2010.2042296 – reference: JumarieGAn approach via fractional analysis to non-linearity induced by coarse-graining in spaceNonlinear Anal. Real World Appl.2010111535546257057310.1016/j.nonrwa.2009.01.0031195.37054 – reference: LeQVA Tutorial on Deep Learning Part 2: Autoencoders, Convolutional Neural Networks and Recurrent Neural Networks2015CAStanford University Department of Computer Science – reference: T. Wigren, J. Schoukens, Three free data sets for development and benchmarking in nonlinear system identification, in Control Conference (ECC), 2013 European, IEEE, 2013, pp. 2933–2938 – reference: SunWZhaoYLiJZhangLGaoHActive suspension control with frequency band constraints and actuator input delayIEEE Trans. Ind. Electron.201259153053710.1109/TIE.2011.2134057 – reference: MaginROvadiaMModeling the cardiac tissue electrode interface using fractional calculusJ. Vib. Control2008149–101431144210.1177/10775463070874391229.92018 – reference: PengHLongFDingCFeature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancyIEEE Trans. Pattern Anal. Mach. Intell.20052781226123810.1109/TPAMI.2005.159 – reference: RajaMAZChaudharyNITwo-stage fractional least mean square identification algorithm for parameter estimation of carma systemsSignal Process.201510732733910.1016/j.sigpro.2014.06.015 – reference: DoyaKYoshizawaSAdaptive neural oscillator using continuous-time back-propagation learningNeural Netw.19892537538510.1016/0893-6080(89)90022-1 – reference: M. Sundermeyer, I. Oparin, J.L. Gauvain, B. Freiberg, R. Schluter, H. Ney, Comparison of feedforward and recurrent neural network language models, in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2013, pp. 8430–8434 – reference: GolubTRSlonimDKTamayoPHuardCGaasenbeekMMesirovJPCollerHLohMLDowningJRCaligiuriMAMolecular classification of cancer: class discovery and class prediction by gene expression monitoringScience1999286543953153710.1126/science.286.5439.531 – reference: J. An, S. Cho, Hand motion identification of grasp-and-lift task from electroencephalography recordings using recurrent neural networks, in 2016 International Conference on Big Data and Smart Computing (BigComp), IEEE, 2016, pp. 427–429 – reference: A. Mazumder, A. Rakshit, D. Tibarewala, A back-propagation through time based recurrent neural network approach for classification of cognitive eeg states, in 2015 IEEE International Conference on Engineering and Technology (ICETECH), IEEE, 2015, pp. 1–5 – reference: B. Shoaib, I.M. Qureshi, Shafqatullah, Ihsanulhaq, Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction. Chin. Phys. B 23(5), 050503 (2014) – reference: B. Krishna, K. Reddy, Active and passive realization of fractance device of order 1/2. Active Passive Electron. Compon. 2008, 369421 (2008). doi:10.1155/2008/369421 – reference: FairbankMAlonsoEProkhorovDAn equivalence between adaptive dynamic programming with a critic and backpropagation through timeIEEE Trans. Neural Netw. Learn. Syst.201324122088210010.1109/TNNLS.2013.2271778 – reference: H. Sak, A. Senior, K. Rao, F. Beaufays, Fast and accurate recurrent neural network acoustic models for speech recognition. arXiv preprint arXiv:1507.06947 (2015) – reference: TanYHeZTianBA novel generalization of modified lms algorithm to fractional orderIEEE Signal Process. Lett.20152291244124810.1109/LSP.2015.2394301 – reference: SunWZhangYHuangYGaoHKaynakOTransient-performance-guaranteed robust adaptive control and its application to precision motion control systemsIEEE Trans. Ind. Electron.201663106510651810.1109/TIE.2016.2542787 – reference: S. Ravuri, A. Stolcke, Recurrent neural network and lstm models for lexical utterance classification, in Sixteenth Annual Conference of the International Speech Communication Association, 2015 – reference: R.J. Williams, D. Zipser, Gradient-based learning algorithms for recurrent networks and their computational complexity. Backpropagation Theory Archit. Appl. 1, 433–486 (1995) – reference: JumarieGTable of some basic fractional calculus formulae derived from a modified Riemann–Liouville derivative for non-differentiable functionsAppl. Math. Lett.2009223378385248350310.1016/j.aml.2008.06.0031171.26305 – reference: BohannanGWAnalog fractional order controller in temperature and motor control applicationsJ. Vib. Control2008149–1014871498246307410.1177/1077546307087435 – reference: Ken-ichiFYuichiNApproximation of dynamical systems by continuous time recurrent neural networksNeural Netw.1993680180610.1016/S0893-6080(05)80125-X – reference: SommacalLMelchiorPOustaloupACabelguenJMIjspeertAJFractional multi-models of the frog gastrocnemius muscleJ. Vib. Control2008149–101415143010.1177/10775463070874401229.92019 – reference: S. Zheng, S. Jayasumana, B. Romera-Paredes, V. Vineet, Z. Su, D. Du, C. Huang, P.H. Torr, Conditional random fields as recurrent neural networks, in Proceedings of the IEEE International Conference on Computer Vision, 2015, pp. 1529–1537 – reference: N.I. Chaudhary, M.A.Z. Raja, M.S. Aslam, N. Ahmed, Novel generalization of volterra lms algorithm to fractional order with application to system identification. Neural Comput. Appl. (2016). doi:10.1007/s00521-016-2548-5 – reference: Z. Gan, C. Li, R. Henao, D.E. Carlson, L. Carin, Deep temporal sigmoid belief networks for sequence modeling, in Advances in Neural Information Processing Systems 28, eds. by C. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama, R. Garnett (Curran Associates, Inc., 2015), pp. 2467–2475 – reference: A. Joulin, T. Mikolov, Inferring algorithmic patterns with stack-augmented recurrent nets, in Advances in Neural Information Processing Systems 28, eds. by C. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama, R. Garnett (Curran Associates, Inc., 2015), pp. 190–198 – reference: M. Kleinz, T. Osler, A childs garden of fractional derivatives. The College Math Journal 31(2), 82–88 (2000) – reference: G. Parascandolo, H. Huttunen, T. Virtanen, Recurrent neural networks for polyphonic sound event detection in real life recordings. arXiv preprint arXiv:1604.00861 (2016) – reference: W. Chan, N. Jaitly, Q.V. Le, O. Vinyals, Listen, attend and spell: a neural network for large vocabulary conversational speech recognition, in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016 – reference: M. Hermans, M. Soriano, J. Dambre, P. Bienstman, I. Fischer, Photonic delay systems as machine learning implementations. arXiv preprint arXiv:1501.02592 (2015) – reference: PandaRDashMFractional generalized splines and signal processingSignal Process.20068692340235010.1016/j.sigpro.2005.10.0171172.65315 – reference: Y. Ji, G. Haffari, J. Eisenstein, A latent variable recurrent neural network for discourse relation language models. arXiv preprint arXiv:1603.01913 (2016) – reference: J. Koscak, R. Jaksa, P. Sincák, Prediction of temperature daily profile by stochastic update of backpropagation through time algorithm. J. Math. Syst. Sci. 2(4), 217–225 (2012) – reference: Y. Pu, X. Yuan, K. Liao, J. Zhou, N. Zhang, X. Pu, Y. Zeng, A recursive two-circuits series analog fractance circuit for any order fractional calculus, in ICO20: Optical Information Processing, 60271Y (2006). doi:10.1117/12.668189 – reference: JumarieGOn the derivative chain-rules in fractional calculus via fractional difference and their application to systems modellingOpen Phys.201311661763310.2478/s11534-013-0256-7 – reference: C. Weng, D. Yu, S. Watanabe, B.H.F. Juang, Recurrent deep neural networks for robust speech recognition, in 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2014, pp. 5532–5536 – reference: GeorgeKSubramanianKSheshadhriNImproving transient response in adaptive control of nonlinear systemsIFAC PapersOnLine201649165866310.1016/j.ifacol.2016.03.131 – reference: WilliamsRJPengJAn efficient gradient-based algorithm for on-line training of recurrent network trajectoriesNeural Comput.19902449050110.1162/neco.1990.2.4.490 – reference: J. Ahmad, Design of Efficient Adaptive Beamforming Algorithms for Novel Mimo Architectures, Ph.D. Thesis, Iqra University, Karachi (2014) – reference: AntoneloEACamponogaraEPlucenioASystem identification of a vertical riser model with echo state networksIFAC PapersOnLine201548630431010.1016/j.ifacol.2015.08.048 – reference: DebnathLRecent applications of fractional calculus to science and engineeringInt. J. Math. Math. Sci.200320035434133442202556610.1155/S01611712033014861036.26004 – reference: H. Jaeger, Tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and the “echo state network” approach, GMD Report 159, (German National Research Center for Information Technology, 2002), p. 48 – reference: Q.V. Le, N. Jaitly, G.E. Hinton, A simple way to initialize recurrent networks of rectified linear units. arXiv preprint arXiv:1504.00941 (2015) – reference: T. Mikolov, A. Joulin, S. Chopra, M. Mathieu, M. Ranzato, Learning longer memory in recurrent neural networks. arXiv preprint arXiv:1412.7753 (2014) – reference: SabatierJAgrawalOPMachadoJTAdvances in Fractional Calculus2007BerlinSpringer10.1007/978-1-4020-6042-71116.00014 – reference: WigrenTRecursive prediction error identification and scaling of non-linear state space models using a restricted black box parameterizationAutomatica2006421159168218307810.1016/j.automatica.2005.08.0171121.93316 – reference: BaoGZengZGlobal asymptotical stability analysis for a kind of discrete-time recurrent neural network with discontinuous activation functionsNeurocomputing201619324224910.1016/j.neucom.2016.02.017 – reference: P.K. Muthukumar, A.W. Black, Recurrent neural network postfilters for statistical parametric speech synthesis. arXiv preprint arXiv:1601.07215 (2016) – reference: M. Weilbeer, Efficient numerical methods for fractional differential equations and their analytical background. Papierflieger (Braunschweig University of Technology, Braunschweig, 2005) – reference: M. Zhang, Z. McCarthy, C. Finn, S. Levine, P. Abbeel, Learning deep neural network policies with continuous memory states. arXiv preprint arXiv:1507.01273 (2015) – reference: HermansMDambreJBienstmanPOptoelectronic systems trained with backpropagation through timeIEEE Trans. Neural Netw. Learn. Syst.201526715451550347992210.1109/TNNLS.2014.2344002 – reference: HaykinSONeural Networks: A Comprehensive Foundation1994Upper Saddle RiverPrentice Hall PTR0828.68103 – reference: SahaSRaghavaGPrediction of continuous b-cell epitopes in an antigen using recurrent neural networkProteins Struct. Funct. Bioinform.2006651404810.1002/prot.21078 – reference: CerveraJBañosAAutomatic loop shaping in qft using crone structuresJ. Vib. Control2008149–1015131529246296310.1177/10775463070874331229.93069 – reference: GrauINápolesGBonetIGarcíaMMBackpropagation through time algorithm for training recurrent neural networks using variable length instancesComput. Sist.20131711524 – reference: JumarieGModified Riemann–Liouville derivative and fractional taylor series of nondifferentiable functions further resultsComput. Math. Appl.200651913671376223763410.1016/j.camwa.2006.02.0011137.65001 – reference: LovoieJOslerTJTremblayRFractional derivatives and special functionsSIAM Rev.197618224026840991410.1137/10180420324.44002 – volume: 49 start-page: 658 issue: 1 year: 2016 ident: 572_CR15 publication-title: IFAC PapersOnLine doi: 10.1016/j.ifacol.2016.03.131 – ident: 572_CR36 – ident: 572_CR40 doi: 10.1109/ICETECH.2015.7275027 – volume: 2 start-page: 490 issue: 4 year: 1990 ident: 572_CR66 publication-title: Neural Comput. doi: 10.1162/neco.1990.2.4.490 – ident: 572_CR46 doi: 10.1117/12.668189 – ident: 572_CR42 – ident: 572_CR48 doi: 10.1109/ICASSP.2016.7472844 – ident: 572_CR44 doi: 10.1109/ICASSP.2016.7472917 – ident: 572_CR63 doi: 10.1109/ICASSP.2014.6854661 – ident: 572_CR9 doi: 10.1007/s00521-016-2548-5 – ident: 572_CR34 doi: 10.1155/2008/369421 – ident: 572_CR23 – ident: 572_CR2 doi: 10.1109/ICCSCE.2016.7893626 – volume: 22 start-page: 1244 issue: 9 year: 2015 ident: 572_CR60 publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2015.2394301 – volume: 2003 start-page: 3413 issue: 54 year: 2003 ident: 572_CR11 publication-title: Int. J. Math. Math. Sci. doi: 10.1155/S0161171203301486 – ident: 572_CR33 – volume-title: Advances in Fractional Calculus year: 2007 ident: 572_CR50 doi: 10.1007/978-1-4020-6042-7 – ident: 572_CR55 doi: 10.1109/ICASSP.2015.7178896 – volume: 22 start-page: 378 issue: 3 year: 2009 ident: 572_CR26 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2008.06.003 – volume: 14 start-page: 1487 issue: 9–10 year: 2008 ident: 572_CR6 publication-title: J. Vib. Control doi: 10.1177/1077546307087435 – volume: 286 start-page: 531 issue: 5439 year: 1999 ident: 572_CR16 publication-title: Science doi: 10.1126/science.286.5439.531 – volume-title: Neural Networks: A Comprehensive Foundation year: 1994 ident: 572_CR18 – ident: 572_CR22 doi: 10.18653/v1/N16-1037 – volume: 193 start-page: 242 year: 2016 ident: 572_CR5 publication-title: Neurocomputing doi: 10.1016/j.neucom.2016.02.017 – volume: 11 start-page: 617 issue: 6 year: 2013 ident: 572_CR28 publication-title: Open Phys. doi: 10.2478/s11534-013-0256-7 – ident: 572_CR53 doi: 10.1088/1674-1056/23/5/050503 – ident: 572_CR59 doi: 10.1109/ICASSP.2013.6639310 – ident: 572_CR68 – volume: 6 start-page: 801 year: 1993 ident: 572_CR30 publication-title: Neural Netw. doi: 10.1016/S0893-6080(05)80125-X – ident: 572_CR70 doi: 10.1109/ICCV.2015.179 – volume: 48 start-page: 304 issue: 6 year: 2015 ident: 572_CR4 publication-title: IFAC PapersOnLine doi: 10.1016/j.ifacol.2015.08.048 – ident: 572_CR3 doi: 10.1109/BIGCOMP.2016.7425963 – ident: 572_CR65 doi: 10.23919/ECC.2013.6669201 – volume: 19 start-page: 416 issue: 2 year: 2011 ident: 572_CR56 publication-title: IEEE Trans. Control Syst. Technol. doi: 10.1109/TCST.2010.2042296 – volume: 24 start-page: 2088 issue: 12 year: 2013 ident: 572_CR13 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2013.2271778 – ident: 572_CR1 – volume: 51 start-page: 1367 issue: 9 year: 2006 ident: 572_CR25 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2006.02.001 – volume: 14 start-page: 1513 issue: 9–10 year: 2008 ident: 572_CR7 publication-title: J. Vib. Control doi: 10.1177/1077546307087433 – ident: 572_CR8 doi: 10.1109/ICASSP.2016.7472621 – volume-title: A Tutorial on Deep Learning Part 2: Autoencoders, Convolutional Neural Networks and Recurrent Neural Networks year: 2015 ident: 572_CR35 – ident: 572_CR21 – volume: 14 start-page: 1415 issue: 9–10 year: 2008 ident: 572_CR54 publication-title: J. Vib. Control doi: 10.1177/1077546307087440 – volume: 26 start-page: 1545 issue: 7 year: 2015 ident: 572_CR19 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2014.2344002 – volume: 17 start-page: 15 issue: 1 year: 2013 ident: 572_CR17 publication-title: Comput. Sist. – volume: 65 start-page: 40 issue: 1 year: 2006 ident: 572_CR51 publication-title: Proteins Struct. Funct. Bioinform. doi: 10.1002/prot.21078 – volume: 42 start-page: 159 issue: 1 year: 2006 ident: 572_CR64 publication-title: Automatica doi: 10.1016/j.automatica.2005.08.017 – ident: 572_CR67 – volume: 14 start-page: 1431 issue: 9–10 year: 2008 ident: 572_CR39 publication-title: J. Vib. Control doi: 10.1177/1077546307087439 – volume: 86 start-page: 2340 issue: 9 year: 2006 ident: 572_CR43 publication-title: Signal Process. doi: 10.1016/j.sigpro.2005.10.017 – volume: 11 start-page: 535 issue: 1 year: 2010 ident: 572_CR27 publication-title: Nonlinear Anal. Real World Appl. doi: 10.1016/j.nonrwa.2009.01.003 – ident: 572_CR61 doi: 10.1109/ICASSP.2016.7472841 – volume: 27 start-page: 1226 issue: 8 year: 2005 ident: 572_CR45 publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2005.159 – ident: 572_CR69 doi: 10.1109/ICRA.2016.7487174 – volume: 2 start-page: 375 issue: 5 year: 1989 ident: 572_CR12 publication-title: Neural Netw. doi: 10.1016/0893-6080(89)90022-1 – ident: 572_CR62 – ident: 572_CR32 doi: 10.2307/2687575 – ident: 572_CR41 – ident: 572_CR10 doi: 10.21437/Interspeech.2015-696 – ident: 572_CR29 – ident: 572_CR52 doi: 10.21437/Interspeech.2015-350 – ident: 572_CR20 – ident: 572_CR31 doi: 10.1007/s00034-016-0375-7 – volume: 18 start-page: 240 issue: 2 year: 1976 ident: 572_CR38 publication-title: SIAM Rev. doi: 10.1137/1018042 – volume: 35 start-page: 110 year: 2015 ident: 572_CR49 publication-title: Curr. Opin. Neurobiol. doi: 10.1016/j.conb.2015.07.006 – ident: 572_CR24 – volume: 59 start-page: 530 issue: 1 year: 2012 ident: 572_CR58 publication-title: IEEE Trans. Ind. Electron. doi: 10.1109/TIE.2011.2134057 – volume: 107 start-page: 327 year: 2015 ident: 572_CR47 publication-title: Signal Process. doi: 10.1016/j.sigpro.2014.06.015 – volume: 11 start-page: 1079 issue: 9 year: 2007 ident: 572_CR37 publication-title: JACIII doi: 10.20965/jaciii.2007.p1079 – ident: 572_CR14 – volume: 63 start-page: 6510 issue: 10 year: 2016 ident: 572_CR57 publication-title: IEEE Trans. Ind. Electron. doi: 10.1109/TIE.2016.2542787 |
| SSID | ssj0019492 |
| Score | 2.3451498 |
| Snippet | In this research, we propose a novel algorithm for learning of the recurrent neural networks called as the fractional back-propagation through time (FBPTT).... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 593 |
| SubjectTerms | Algorithms Back propagation Back propagation networks Chaos theory Circuits and Systems Electrical Engineering Electronics and Microelectronics Engineering Fractional calculus Instrumentation Machine learning Neural networks Nonlinear systems Recurrent neural networks Signal,Image and Speech Processing System identification |
| SummonAdditionalLinks | – databaseName: SpringerLink Journals (ICM) dbid: U2A link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDLZgXOCAeIrBQDlwAkVqkzZtjgUxJiR2mJi0W9Um2UAa29QVDvv1OH0xECBxruODE9tfavsLwKV0tEHUr2ioE04RgaNLBUxQwRyTBHhv5qkdTn7si97Qexj5o2qOe1l3u9clySJSN8NuBZcKtVEVMQajq03Y8i2bFx7iIYua0oH0ipeQbUWNYr4b1aXMn1R8TUafCPNbUbTINd092K1AIonKXd2HDTM7gJ016sBDGESkP383U9LNytEElL_Piv6tnN5gatKkok6dkGg6mWcv-fMrQYRKBvYPu-VkIpaYA5f1y07w5REMu3dPtz1avY9AFXdFTtk4FXLsK6OkVKE0XPjMGMHSNEn8NNGuctPA-phUiMtM4PmWL9DhmvsaA6Hmx9CazWfmBAg3oWvGjhcYbSuhoQxRNfeEDhPP9bRqg1MbKlYVebh9w2IaN7THhW1jtG1sbRuv2nDVLFmUzBl_CXdq68eVEy1j21uIiIwztw3X9Y6sff5N2em_pM9gG0FQWHZid6CVZ2_mHIFGnl4UB-sDXBDI8w priority: 102 providerName: Springer Nature |
| Title | A Novel Fractional Gradient-Based Learning Algorithm for Recurrent Neural Networks |
| URI | https://link.springer.com/article/10.1007/s00034-017-0572-z https://www.proquest.com/docview/1993256321 |
| Volume | 37 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVEBS databaseName: EBSCOhost Mathematics Source - trial do 30.11.2025 customDbUrl: eissn: 1531-5878 dateEnd: 20241102 omitProxy: false ssIdentifier: ssj0019492 issn: 0278-081X databaseCode: AMVHM dateStart: 20110201 isFulltext: true titleUrlDefault: https://www.ebsco.com/products/research-databases/mathematics-source providerName: EBSCOhost – providerCode: PRVPQU databaseName: PROQUEST customDbUrl: http://www.proquest.com/pqcentral?accountid=15518 eissn: 1531-5878 dateEnd: 20241102 omitProxy: true ssIdentifier: ssj0019492 issn: 0278-081X databaseCode: BENPR dateStart: 19970101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Technology Collection customDbUrl: eissn: 1531-5878 dateEnd: 20241102 omitProxy: true ssIdentifier: ssj0019492 issn: 0278-081X databaseCode: 8FG dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/technologycollection1 providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK - Czech Republic Consortium customDbUrl: eissn: 1531-5878 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0019492 issn: 0278-081X databaseCode: AGYKE dateStart: 19970101 isFulltext: true titleUrlDefault: http://link.springer.com providerName: Springer Nature – providerCode: PRVAVX databaseName: SpringerLink Journals (ICM) customDbUrl: eissn: 1531-5878 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0019492 issn: 0278-081X databaseCode: U2A dateStart: 19970101 isFulltext: true titleUrlDefault: http://www.springerlink.com/journals/ providerName: Springer Nature |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3JTsMwEB1Be4EDYhVlqXzgBLJI7KwHhAJqi0BEqKJSOUWJ7ZZDaaEEDnw9M1nKIsE1sS1lvMyLZ-Y9gKPQ0gZRv-KBTiVHBI5byhce94RlUh__m2VGxcm3sXc1cK6H7nAJ4roWhtIq6zOxOKj1TNEd-SklmqF7lsI-f37hpBpF0dVaQiOtpBX0WUExtgxNQcxYDWhedOK7_iKuEDqFTDKF2zg6w2Ed57QKWlFLUkaGzxHDCP7x01N9wc9fEdPCEXXXYa1CkCwqp3wDlsx0E1a_8QpuQT9i8ezdTFh3XtYtYPvevEjuyvkF-i3NKl7VMYsmY_zM_PGJIXxlfbp-J8ImRqwd2C0u08Rft2HQ7dxfXvFKPIEraXs5F6PMC0euMioMVRAa6bnCGE9kWZq6WaptZWc-bcBQIWgzvuMSmaAltXQ1npJa7kBjOpuaXWDSBLYZWY5vNIVJgzDAoaXj6SB1bEerFli1oRJVMYuTwMUkWXAiF7ZN0LYJ2Tb5aMHxostzSavxX-OD2vpJtcNek6_10IKTeka-vf5rsL3_B9uHFRKUL7PIDqCRz9_MIcKOPGvDctDttaEZ9R5uOu1qZeHTgYg-AZaS1eE |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LTxsxEB6FcIAeKlpApDzqQ3sBWeza3ocPqAqUEAqsUARSbsuu7aSHNAnJFlR-HL-N8T4SigQ3zrbnMB57PntmvgH4Jh1tEPUrGuqEU0TgeKQC5lOfOSYJ8N3MU1ucfBH57Wvxq-t1a_BY1cLYtMrqTswvaj1S9o983yaaoXvmzP0xvqW2a5SNrlYtNJKytYI-yCnGysKOM_PvHp9w04PTn7jf3xlrHV8dtWnZZYAq7voZZb3Ulz1PGSWlCqXhvseM8VmaJomXJtpVbhpYS5UK0Y0JhGdZ9xyuuafxOtEc5S7AouBC4uNv8fA4uuzM4hhS5G2ZbXiPovPtVnFVJ6cxdbjNAAkoYiZGH_73jHO4-yJCmzu-1gp8LBEraRYm9glqZvgZPjzjMVyFTpNEozszIK1JUSeB808meTJZRg_RT2pS8rj2SXPQR7Vmv_8QhMukY7_7LUEUsSwhuCwq0tKna3D9Lmpch_pwNDQbQLgJXdNzRGC0DcuGMkTRXPg6TIQrtGqAUykqViWTuW2oMYhnHMy5bmPUbWx1Gz80YHe2ZFzQeLw1eavSflye6Gk8t78G7FU78mz4NWFf3hb2FZbaVxfn8flpdLYJywjHwiInfAvq2eSv2UbIk6U7pV0RuHlvU34C_wwPMg |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LTxsxEB5RkKpyqIC2IiWAD3ApsrJr7_OAqvDY8GqEokbKbbtre-GQJpBsW5Gf1l_HzD7CQ4IbZ9tzGI89nz0z3wDshJY2iPoVD3QiOSJwPFK-8LgnLJP4-G6WKRUn_-h6J33nbOAOFuB_XQtDaZX1nVhc1Hqs6I-8RYlm6J6lsFtZlRZxeRR9v7nl1EGKIq11O43SRM7N3T98vk33T49wr3eFiI5_Hp7wqsMAV9L2ci6y1AszVxkVhioIjfRcYYwn0jRJ3DTRtrJTn6w0VIhsjO-4xLhnSS1djVeJlij3HSz5xOJOVepRZx7BCJ2iITMF9ji63UEdUbUKAlNLUu6HzxEtCT576hMfgO6z2Gzh8qIV-FhhVdYujWsVFsxoDZYfMRh-gl6bdcd_zZBFk7JCAud3JkUaWc4P0ENqVjG4XrH28AqVmF__ZgiUWY8--okaihE_CC7rlgnp08_QfxMlfoHF0Xhk1oFJE9gmsxzfaArIBmGAoqXj6SBxbEerBli1omJVcZhTK41hPGdfLnQbo25j0m08a8C3-ZKbksDjtcnNWvtxdZan8YPlNWCv3pFHwy8J-_q6sG14jwYcX5x2zzfgA-KwoEwGb8JiPvljNhHr5OlWYVQMfr21Fd8DhlgMzA |
| 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=A+Novel+Fractional+Gradient-Based+Learning+Algorithm+for+Recurrent+Neural+Networks&rft.jtitle=Circuits%2C+systems%2C+and+signal+processing&rft.au=Khan%2C+Shujaat&rft.au=Ahmad%2C+Jawwad&rft.au=Naseem%2C+Imran&rft.au=Moinuddin%2C+Muhammad&rft.date=2018-02-01&rft.issn=0278-081X&rft.eissn=1531-5878&rft.volume=37&rft.issue=2&rft.spage=593&rft.epage=612&rft_id=info:doi/10.1007%2Fs00034-017-0572-z&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s00034_017_0572_z |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0278-081X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0278-081X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0278-081X&client=summon |