Abstract
The scope of this study is to present a complete statistical framework for model identification of wavelet neural networks (WN). In each step in WN construction we test various methods already proposed in literature. In the first part we compare four different methods for the initialization and construction of the WN. Next various information criteria as well as sampling techniques proposed in previous works were compared to derive an algorithm for selecting the correct topology of a WN. Finally, in variable significance testing the performance of various sensitivity and model-fitness criteria were examined and an algorithm for selecting the significant explanatory variables is presented.
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References
Pati, Y., Krishnaprasad, P.: Analysis and Synthesis of Feedforward Neural Networks Using Discrete Affine Wavelet Transforms. IEEE Trans. on Neural Networks 4(1), 73–85 (1993)
Zhang, Q., Benveniste, A.: Wavelet Networks. IEEE Trans. on Neural Networks 3(6), 889– 898 (1992)
Bernard, C., Mallat, S., Slotine, J.-J.: Wavelet Interpolation Networks. In Proc. ESANN ′98, 47–52 (1998)
Benaouda, D., Murtagh, G., Starck, J.-L., Renaud, O.: Wavelet-Based Nonlinear Multiscale Decomposition Model for Electricity Load Forecasting. Neurocomputing 70, 139–154 (2006)
Chen, Y., Yang, B., Dong, J.: Time-Series Prediction Using a Local Linear Wavelet Neural Wavelet. Neurocomputing 69, 449–465 (2006)
Kadambe, S., Srinivasan, P.: Adaptive Wavelets for Signal Classification and Compression. International Journal of Electronics and Communications 60, 45–55 (2006)
Billings, S., Wei, H.-L.: A New Class of Wavelet Networks for Nonlinear System Identification. IEEE Trans. on Neural Networks 16(4), 862–874 (2005)
Jiao, L., Pan, J., Fang, Y.: Multiwavelet Neural Network and Its Approximation Properties. IEEE Trans. on Neural Networks 12(5), 1060–1066 (2001)
Khayamian, T., Ensafi, A., Tabaraki, R., Esteki, M.: Principal Component-Wavelet Networks as a New Multivariate Calibration Model. Analytical Letters 38(9), 1447–1489 (2005)
Zapranis, A., Alexandridis, A.: Modelling Temperature Time Dependent Speed of Mean Reversion in the Context of Weather Derivetive Pricing. Applied Mathematical Finance 15(4), 355 – 386 (2008)
Zapranis, A., Alexandridis, A.: Weather Derivatives Pricing: Modelling the Seasonal Residuals Variance of an Ornstein-Uhlenbeck Temperature Process with Neural Networks. Neurocomputing (accepted, to appear) (2007)
Becerikli, Y.: On Three Intelligent Systems: Dynamic Neural, Fuzzy and Wavelet Networks for Training Trajectory. Neural Computation and Applications. 13, 339–351 (2004)
Zhao, J., Chen, B., Shen, J.: Multidimensional Non-Orthogonal Wavelet-Sigmoid Basis Function Neurla Network for Dynamic Process Fault Diagnosis. Computers and Chemical Engineering 23, 83–92 (1998)
Zhang, Q.: Using Wavelet Network in Nonparametric Estimation. IEEE Trans. on Neural Networks 8(2), 227–236 (1997)
Oussar, Y., Rivals, I., Presonnaz, L., Dreyfus, G.: Trainning Wavelet Networks for Nonlinear Dynamic Input Output Modelling. Neurocomputing 20, 173–188 (1998)
Postalcioglu, S., Becerikli, Y.: Wavelet Networks for Nonlinear System Modelling. Neural Computing & Applications 16, 434–441 (2007)
Oussar, Y., Dreyfus, G.: Initialization by Selection for Wavelet Network Training. Neurocomputing 34, 131–143 (2000)
Xu, J., Ho, D.: A Basis Selection Algorithm for Wavelet Neural Networks. Neurocomputing 48, 681–689 (2002)
Gao, R., Tsoukalas, H.: Neural-wavelet Methodology for Load Forecasting. Journal of Intelligent & Robotic Systems 31, 149–157 (2001)
Xu, J., Ho, D.: A Constructive Algorithm for Wavelet Neural Networks. Lecture Notes in Computer Science(3610), 730–739 (2005)
Kan, K.-C., Wong, K.: Self-construction algorithm for synthesis of wavelet networks. Electronic Letters 34, 1953–1955 (1998)
Li, S., Chen, S.-C.: Function Approximation using Robust Wavelet Neural Networks. In Proc. ICTAI ′02, 483–488 (2002)
Efron, B., Tibshirani, R.: An Introduction to the Bootstrap. Chapman & Hall, USA (1993)
Zapranis, A., Refenes, A.: Principles of Neural Model Indentification, Selection and Adequacy: With Applications to Financial Econometrics. Springer-Verlag (1999)
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Zapranis, A., Alexandridis, A. (2009). Model Identification in Wavelet Neural Networks Framework. In: Iliadis, Maglogiann, Tsoumakasis, Vlahavas, Bramer (eds) Artificial Intelligence Applications and Innovations III. AIAI 2009. IFIP International Federation for Information Processing, vol 296. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0221-4_32
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DOI: https://doi.org/10.1007/978-1-4419-0221-4_32
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