Abstract
Least Squares Support Vector Regression (LS-SVR) is a powerful kernel-based learning tool for regression problems. Nonlinear system identification is one of such problems where we aim at capturing the behavior in time of a dynamical system by building a black-box model from the measured input-output time series. Besides the difficulties involved in the specification a suitable model itself, most real-world systems are subject to the presence of outliers in the observations. Hence, robust methods that can handle outliers suitably are desirable. In this regard, despite the existence of a few previous works on robustifying the LS-SVR for regression applications with outliers, its use for dynamical system identification has not been fully evaluated yet. Bearing this in mind, in this paper we assess the performances of two existing robust LS-SVR variants, namely WLS-SVR and RLS-SVR, in nonlinear system identification tasks containing outliers. These robust approaches are compared with standard LS-SVR in experiments with three artificial datasets, whose outputs are contaminated with different amounts of outliers, and a real-world benchmarking dataset. The obtained results for infinite step ahead prediction confirm that the robust LS-SVR variants consistently outperforms the standard LS-SVR algorithm.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cai, Y., Wang, H., Ye, X., Fan, Q.: A multiple-kernel lssvr method for separable nonlinear system identification. Journal of Control Theory and Applications 11(4), 651–655 (2013)
Chapelle, O.: Training a support vector machine in the primal. Neural Computation 19(5), 1155–1178 (2007)
Falck, T., Dreesen, P., De Brabanter, K., Pelckmans, K., De Moor, B., Suykens, J.A.: Least-squares support vector machines for the identification of wiener-hammerstein systems. Control Engineering Practice 20(11), 1165–1174 (2012)
Falck, T., Suykens, J.A., De Moor, B.: Robustness analysis for least squares kernel based regression: an optimization approach. In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009 Held Jointly with the 2009 28th Chinese Control Conference, CDC/CCC 2009, pp. 6774–6779. IEEE (2009)
Huber, P.J., et al.: Robust estimation of a location parameter. The Annals of Mathematical Statistics 35(1), 73–101 (1964)
Khalil, H.M., El-Bardini, M.: Implementation of speed controller for rotary hydraulic motor based on LS-SVM. Expert Systems with Applications 38(11), 14249–14256 (2011)
Kocijan, J., Girard, A., Banko, B., Murray-Smith, R.: Dynamic systems identification with Gaussian processes. Mathematical and Computer Modelling of Dynamical Systems 11(4), 411–424 (2005)
Liu, Y., Chen, J.: Correntropy-based kernel learning for nonlinear system identification with unknown noise: an industrial case study. In: 2013 10th India International Symposium on Dynamics and Control of Proccess Systems, pp. 361–366 (2013)
Liu, Y., Chen, J.: Correntropy kernel learning for nonlinear system identification with outliers. Industrial and Enginnering Chemistry Research pp. 1–13 (2013)
Ljung, L.: System Identification Theory for the User. 2nd edn. (1999)
Majhi, B., Panda, G.: Robust identification of nonlinear complex systems using low complexity ANN and particle swarm optimization technique. Expert Systems with Applications 38(1), 321–333 (2011)
Narendra, K.S., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks 1(1), 4–27 (1990)
Rousseeum, P.J., Leroy, A.M.: Robust Regression and Outlier Detection. 1st edn. (1987)
Saunders, C., Gammerman, A., Vovk, V.: Ridge regression learning algorithm in dual variables. In: Proceedings of the 15th International Conference on Machine Learning, ICML 1998, pp. 515–521. Morgan Kaufmann (1998)
Suykens, J.A.K., Van Gestel, T., De Brabanter, J., De Moor, B., Vandewalle, J.: Least Squares Support Vector Machines, 1st edn. World Scientific Publishing (2002)
Suykens, J.A.K., Vandewalle, J.: Least squares support vector machine classifiers. Neural Processing Letters 9(3), 293–300 (1999)
Suykens, J.A., De Brabanter, J., Lukas, L., Vandewalle, J.: Weighted least squares support vector machines: robustness and sparse approximation. Neurocomputing 48(1), 85–105 (2002)
Van Gestel, T., Suykens, J.A., Baestaens, D.E., Lambrechts, A., Lanckriet, G., Vandaele, B., De Moor, B., Vandewalle, J.: Financial time series prediction using least squares support vector machines within the evidence framework. IEEE Transactions on Neural Networks 12(4), 809–821 (2001)
Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer (1995)
Yang, X., Tan, L., He, L.: A robust least squares support vector machine for regression and classification with noise. Neurocomputing 140, 41–52 (2014)
Yuille, A.L., Rangarajan, A.: The concave-convex procedure. Neural Computation 15(4), 915–936 (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Santos, J.D.A., Mattos, C.L.C., Barreto, G.A. (2015). Performance Evaluation of Least Squares SVR in Robust Dynamical System Identification. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2015. Lecture Notes in Computer Science(), vol 9095. Springer, Cham. https://doi.org/10.1007/978-3-319-19222-2_36
Download citation
DOI: https://doi.org/10.1007/978-3-319-19222-2_36
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19221-5
Online ISBN: 978-3-319-19222-2
eBook Packages: Computer ScienceComputer Science (R0)