Least Squares Support Vector Machine Based on Wavelet-Neuron

Yevgeniy Bodyanskiy, Olena Vynokurova, Oleksandra Kharchenko

Abstract


In this paper, a simple wavelet-neuro-system that implements learning ideas based on minimization of empirical risk and oriented on information processing in on-line mode is developed. As an elementary block of such systems, we propose using wavelet-neuron that has improved approximation properties, computational simplicity, high learning rate and capability of local feature identification in data processing. The architecture and learning algorithm for least squares wavelet support machines that are characterized by high speed of operation and possibility of learning under conditions of short training set are proposed.

Keywords:
Adaptive wavelet function; forecasting; least squares support vector machine; non-linear non-stationary time series; wavelet-neuron

Full Text:

 PDF

References


K.-L. Du and M. N. S. Swamy, Neural Networks and Statistical Learning London: Springer-Verlag, 2014. http://dx.doi.org/10.1007/978- 1-4471-5571-3

S. Haykin, Neural Networks. A Comprehensive Foundation Upper Saddle River, N. J.: Prentice Hall, 1999.

J.-S. R. Jang, “ANFIS: Adaptive-network-based fuzzy inference systems,” IEEE Trans. on Syst. Man. and Cybern., vol. 23, issue 3, pp. 665–685, 1993. http://dx.doi.org/10.1109/21.256541

J.-S. R. Jang, C. T. Sun, and E. Mizutani. Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, N. J.: Prentice Hall, 1997.

O. Nelles, Nonlinear System Identification, Berlin: Springer, 2001. http://dx.doi.org/10.1007/978-3-662-04323-3

E. Uchino and T. Yamakawa, “Soft computing based signal prediction, restoration and filtering,” in Intelligent Hybrid Systems: Fuzzy Logic, Neural Networks and Genetic Algorithms, Da Ruan Eds., Boston: Kluwer Academic Publisher, 1997, pp. 331–349.

Ye. Bodyanskiy and O. Vynokurova, ”Hybrid adaptive wavelet-neuro- fuzzy system for chaotic time series identification,” Information Science, n. 220, pp.170–179, 2013.

L. Ljung, System Identification: Theory for the User, N.Y.: Prentice- Hall, 1999.

C. Cortes and V. Vapnik, “Support vector networks,” Machine Learning, n. 20, pp.273–297, 1995. http://dx.doi.org/10.1007/BF00994018

V.N. Vapnik and A.Ya. Chervonenkis, Pattern Recognition Theory (Statistical Learning Problems), М.: Nauka, 1974. (in Russian).

V. N. Vapnik and A. Ya. Chervonenkis, Empirical Data Dependencies Restoration, М.: Nauka, 1979. (in Russian).

V. N. Vapnik, The Nature of Statistical Learning Theory, N. Y.:

Springer, 1995. http://dx.doi.org/10.1007/978-1-4757-2440-0

J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, and J. Vandewalle. Least Squares Support Vector Machines, Singapore: World Scientific, 2002.

S. Abe and D. Tsujinishi, “Fuzzy Least Squares Support Vector Machines for multiclass problems,” Neural Networks, n. 16, pp. 785– 792, 2003.

Ch.-F. Lin and Sh.-D. Wang, “Fuzzy Support Vector Machines,” IEEE Trans. on Neural Networks, n. 13, pp. 646–671, 2002.

S.M. Pandhiani and A.B. Shabri, “Time Series Forecasting Using Wavelet-Least Squares Support Vector Machines and Wavelet Regression Models for Monthly Stream Flow Data,” Open Journal of Statistics, n. 3, pp. 183–194, 2013.

D. Kumar, R. K. Tripathy and A. Acharya, “Least squares support vector machine based multiclass classification of EEG signals,” WSEAS Transactions on Signal Processing, vol. 10, pp. 86–94, 2014.

D. Zahirniak, R. Chapman, S. K. Rogers, B. W. Suter, M. Kabrisky and V. Pyati, “Pattern recognition using radial basis function network,” in

Application of Artificial Intelligence Conf., Dayton, OH, 1990, pp. 249–260.

T. Yamakawa, “A novel nonlinear synapse neuron model guaranteeing a global minimum – Wavelet neuron,” in Proc. 28th IEEE Int. Symp. On Multiple-Valued Logic, Fukuoka, Japan, IEEE Comp. Soc., 1998, pp. 335–336.

Ye. Bodyanskiy, O. Vynokurova, and O. Kharchenko, “Hybrid cascade neural network based on wavelet-neuron,” Information Theories and Application, vol. 18, no. 4, pp. 335–343, 2011.

Ye. Bodyanskiy, N. Lamonova, I. Pliss, and O. Vynokurova, “An adaptive learning algorithm for a wavelet neural network,” Expert Systems, vol. 22, no. 5, pp. 235–240, 2005. http://dx.doi.org/10.1111/j.1468-0394.2005.00314.x

Ye. Bodyanskiy, I. Pliss, and O. Vynokurova, “Flexible neo-fuzzy neuron and neuro-fuzzy network for monitoring of time series properties,” Scientific J. of Riga Technical University. Information Technology and Management Science, vol. 16, pp. 47–52, 2013.

Ye. Bodyanskiy, O. Vynokurova, E. Yegorova, “Radial-basis-fuzzy- wavelet-neural network with adaptive activation-membership function” Int. J. on Artificial Intelligence and Machine Learning, no. 8 (II), pp. 9–15, 2008.

G. C. Goodwin, P. J. Ramadge, and R. E. Caines, “A globally convergent adaptive predictor,” Automatica, vol. 17, no. 1, pp. 135–140, 1981. http://dx.doi.org/10.1016/0005-1098(81)90089-3

F. R. Gantmacher, The Theory of Matrices AMS, Chelsea Publishing: Reprinted by American Mathematical Society, 2000.

Data Market – the open portal to thousands of datasets [Online]. Available: http://datamarket.com/en/data/set/1loo/#!ds=1loo!1n6s=2qi. 2ql.2qn&display=line&title=Average+monthly+temperatures+across+th e+world+(1701-2011)&s=8gd


Refbacks

  • There are currently no refbacks.


Copyright (c) 2014 Yevgeniy Bodyanskiy, Olena Vynokurova, Oleksandra Kharchenko

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.