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Other Recurrent Neural Networks Models

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Abstract

In this chapter we review two additional types of Recurrent Neural Network, which present important differences with respect to the architectures described so far. More specifically, we introduce the nonlinear auto-regressive with eXogenous inputs (NARX) neural network and the Echo State Network. Both these networks have been largely employed in Short Term Load Forecast applications and they have been shown to be more effective than other methods based on statistical models. The main differences of NARX networks and Echo State Networks with respect to the other previously described models, are both in terms of their architecture and, in particular, in their training procedure. Indeed, both these architectures are designed in such a way that Back Propagation Through Time is not necessary. Specifically, in NARX the network output is replaced by the expected ground truth and this allows to train the network like a feedforward architecture. On the other hand, in a Echo State Network only the outermost linear layer is trained, usually by means of ridge regression. Due to these fundamental differences, some of the properties and training approaches discussed in the previous sections do not hold for the NARX and Echo State Network models and we reserved a separate chapter to review these models.

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References

  • Alexandre LA, Embrechts MJ, Linton J (2009) Benchmarking reservoir computing on time-independent classification tasks. In: 2009 International Joint Conference on Neural Networks, IJCNN 2009. IEEE, pp 89–93

    Google Scholar 

  • Appeltant L, Soriano MC, Van der Sande G, Danckaert J, Massar S, Dambre J, Schrauwen B, Mirasso CR, Fischer I (2011) Information processing using a single dynamical node as complex system. Nature Commun 2:468. https://doi.org/10.1038/ncomms1476

    Article  Google Scholar 

  • Bianchi FM, De Santis E, Rizzi A, Sadeghian A (2015) Short-term electric load forecasting using echo state networks and PCA decomposition. IEEE Access 3:1931–1943. https://doi.org/10.1109/ACCESS.2015.2485943

    Article  Google Scholar 

  • Bianchi FM, Scardapane S, Uncini A, Rizzi A, Sadeghian A (2015) Prediction of telephone calls load using echo state network with exogenous variables. Neural Netw 71:204–213. https://doi.org/10.1016/j.neunet.2015.08.010

    Article  Google Scholar 

  • Bianchi FM, Livi L, Alippi C (2016a) Investigating echo-state networks dynamics by means of recurrence analysis. IEEE Trans Neural Netw Learn Syst 99:1–13. https://doi.org/10.1109/TNNLS.2016.2630802

  • Billings SA (2013) Nonlinear system identification: NARMAX methods in the time, frequency, and spatio-temporal domains. Wiley

    Google Scholar 

  • Boedecker J, Obst O, Lizier JT, Mayer NM, Asada M (2012) Information processing in echo state networks at the edge of chaos. Theory Biosci 131(3):205–213

    Article  Google Scholar 

  • Cambria E, Huang GB, Kasun LLC, Zhou H, Vong CM, Lin J, Yin J, Cai Z, Liu Q, Li K et al (2013) Extreme learning machines [trends & controversies]. IEEE Intell Syst 28(6):30–59

    Article  Google Scholar 

  • Deihimi A, Showkati H (2012) Application of echo state networks in short-term electric load forecasting. Energy 39(1):327–340

    Article  Google Scholar 

  • Deihimi A, Orang O, Showkati H (2013) Short-term electric load and temperature forecasting using wavelet echo state networks with neural reconstruction. Energy 57:382–401

    Article  Google Scholar 

  • Diaconescu E (2008) The use of narx neural networks to predict chaotic time series. Wseas Trans Comput Res 3(3):182–191

    Google Scholar 

  • Filippo MB, Livi L, Alippi C, Jenssen R (2017) Multiplex visibility graphs to investigate recurrent neural network dynamics. Sci Rep 7(44):037. https://doi.org/10.1038/srep4403710.1038/srep44037

    Google Scholar 

  • Gallicchio C, Micheli A, Pedrelli L (2017) Deep reservoir computing: a critical experimental analysis. Neurocomputing. https://doi.org/10.1016/j.neucom.2016.12.089

    Google Scholar 

  • Hai-yan D, Wen-jiang P, Zhen-ya H (2005) A multiple objective optimization based echo state network tree and application to intrusion detection. In: 2005 Proceedings of 2005 IEEE international workshop on VLSI design and video technology, pp 443–446. https://doi.org/10.1109/IWVDVT.2005.1504645

  • Han S, Lee J (2014a) Fuzzy echo state neural networks and funnel dynamic surface control for prescribed performance of a nonlinear dynamic system. IEEE Trans Ind Electron 61(2):1099–1112. https://doi.org/10.1109/TIE.2013.2253072

    Article  Google Scholar 

  • Han SI, Lee JM (2014b) Fuzzy echo state neural networks and funnel dynamic surface control for prescribed performance of a nonlinear dynamic system. IEEE Trans Ind Electron 61(2):1099–1112

    Article  Google Scholar 

  • Huang CM, Huang CJ, Wang ML (2005) A particle swarm optimization to identifying the armax model for short-term load forecasting. IEEE Trans Power Syst 20(2):1126–1133

    Article  Google Scholar 

  • Jaeger H (2001) The “echo state” approach to analysing and training recurrent neural networks-with an erratum note. Technical Report 148:34, German National Research Center for Information Technology GMD, Bonn, Germany

    Google Scholar 

  • Jaeger H, Haas H (2004) Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication. Science 304(5667):78–80. https://doi.org/10.1126/science.1091277

    Article  Google Scholar 

  • Leontaritis I, Billings SA (1985) Input-output parametric models for non-linear systems part i: deterministic non-linear systems. Int J Control 41(2):303–328

    Article  MATH  Google Scholar 

  • Li D, Han M, Wang J (2012a) Chaotic time series prediction based on a novel robust echo state network. IEEE Trans Neural Netw Learn Syst 23(5):787–799

    Article  Google Scholar 

  • Lin T, Horne BG, Tiňo P, Giles CL (1996) Learning long-term dependencies in narx recurrent neural networks. IEEE Trans Neural Netw 7(6):1329–1338

    Article  Google Scholar 

  • Lin TN, Giles CL, Horne BG, Kung SY (1997) A delay damage model selection algorithm for narx neural networks. IEEE Trans Signal Process 45(11):2719–2730

    Article  Google Scholar 

  • Løkse S, Bianchi FM, Jenssen R (2017) Training echo state networks with regularization through dimensionality reduction. Cogn Comput 1–15. https://doi.org/10.1007/s12559-017-9450-z

  • Lukoševičius M, Jaeger H (2009) Reservoir computing approaches to recurrent neural network training. Comput Sci Rev 3(3):127–149. https://doi.org/10.1016/j.cosrev.2009.03.005

    Article  MATH  Google Scholar 

  • Maass W, Natschläger T, Markram H (2002) Real-time computing without stable states: a new framework for neural computation based on perturbations. Neural Comput 14(11):2531–2560. https://doi.org/10.1162/089976602760407955

    Article  MATH  Google Scholar 

  • Maiorino E, Bianchi F, Livi L, Rizzi A, Sadeghian A (2017) Data-driven detrending of nonstationary fractal time series with echo state networks. Inf Sci 382–383:359–373. https://doi.org/10.1016/j.ins.2016.12.015

    Article  Google Scholar 

  • Mazumdar J, Harley R (2008) Utilization of echo state networks for differentiating source and nonlinear load harmonics in the utility network. IEEE Trans Power Electron 23(6):2738–2745. https://doi.org/10.1109/TPEL.2008.2005097

    Article  Google Scholar 

  • Menezes JMP, Barreto GA (2008) Long-term time series prediction with the narx network: an empirical evaluation. Neurocomputing 71(16):3335–3343

    Article  Google Scholar 

  • Napoli R, Piroddi L (2010) Nonlinear active noise control with narx models. IEEE Trans Audio, Speech, and Lang Process 18(2):286–295

    Article  Google Scholar 

  • Niu D, Ji L, Xing M, Wang J (2012) Multi-variable echo state network optimized by Bayesian regulation for daily peak load forecasting. J Netw 7(11):1790–1795

    Google Scholar 

  • Peng Y, Lei M, Li JB, Peng XY (2014) A novel hybridization of echo state networks and multiplicative seasonal ARIMA model for mobile communication traffic series forecasting. Neural Comput Appl 24(3–4):883–890

    Article  Google Scholar 

  • Plett GL (2003) Adaptive inverse control of linear and nonlinear systems using dynamic neural networks. IEEE Trans Neural Netw 14(2):360–376

    Article  Google Scholar 

  • Rodan A, Tiňo P (2011) Minimum complexity echo state network. IEEE Trans Neural Netw 22(1):131–144. https://doi.org/10.1109/TNN.2010.2089641

    Article  Google Scholar 

  • Rodan A, Tiňo P (2012) Simple deterministically constructed cycle reservoirs with regular jumps. Neural Comput 24(7):1822–1852. https://doi.org/10.1162/NECO_a_00297

    Article  MathSciNet  Google Scholar 

  • Scardapane S, Comminiello D, Scarpiniti M, Uncini A (2015) Online sequential extreme learning machine with kernels. IEEE Trans Neural Netw Learn Syst 26(9):2214–2220. https://doi.org/10.1109/TNNLS.2014.2382094

    Article  MathSciNet  Google Scholar 

  • Siegelmann HT, Horne BG, Giles CL (1997) Computational capabilities of recurrent narx neural networks. IEEE Trans Syst Man Cybern Part B: Cybern 27(2):208–215

    Article  Google Scholar 

  • Skowronski MD, Harris JG (2007) Automatic speech recognition using a predictive echo state network classifier. Neural Netw 20(3):414–423

    Article  MATH  Google Scholar 

  • Varshney S, Verma T (2014) Half hourly electricity load prediction using echo state network. Int J Sci Res 3(6):885–888

    Google Scholar 

  • Verstraeten D, Schrauwen B (2009) On the quantification of dynamics in reservoir computing. In: Alippi C, Polycarpou M, Panayiotou C, Ellinas G (eds) Artificial neural networks—ICANN 2009, vol 5768. Springer, Berlin, pp 985–994. https://doi.org/10.1007/978-3-642-04274-4_101

  • Xie H, Tang H, Liao YH (2009) Time series prediction based on narx neural networks: An advanced approach. In: 2009 International conference on machine learning and cybernetics, vol 3, pp 1275–1279. https://doi.org/10.1109/ICMLC.2009.5212326

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Correspondence to Filippo Maria Bianchi .

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Bianchi, F.M., Maiorino, E., Kampffmeyer, M.C., Rizzi, A., Jenssen, R. (2017). Other Recurrent Neural Networks Models. In: Recurrent Neural Networks for Short-Term Load Forecasting. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-70338-1_4

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  • DOI: https://doi.org/10.1007/978-3-319-70338-1_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70337-4

  • Online ISBN: 978-3-319-70338-1

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