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Title: Design and analysis for wavelet neural network identification model
Other Titles: Xiao bo shen jing wang lu bian shi mo xing zhi she ji ji fen xi
Authors: Yeung, Loi Leung (楊來樑)
Department: Dept. of Mathematics
Degree: Master of Philosophy
Issue Date: 2005
Publisher: City University of Hong Kong
Subjects: Neural networks (Computer science)
Wavelets (Mathematics)
Notes: 132 leaves : ill. ; 30 cm.
CityU Call Number: QA76.87.Y48 2005
Includes bibliographical references (leaves 128-132)
Thesis (M.Phil.)--City University of Hong Kong, 2005
Type: Thesis
Abstract: In the past decades, neural networks have been established as a general approximation tool for fitting nonlinear models from input-output data. A neural network derives its computing power through its massively parallel distributed structure and its ability to learn, therefore forming an ideal identification tool. However, the implementation of neural networks suffers from the lack of efficient constructive methods, both for determining the parameters of neurons and for choosing network structures. To design efficient constructive methods for determining the parameters of neurons and for choosing effective network structures, four essential factors are considered in this thesis. They are shown as follows: Factor 1. activation function in neurons:- its characteristics benefits for systemically constructing networks and networks’ approximation ability. Factor 2. network parameter settings:- it can not only allow the network to be fine-tuned, but also filter unsignificant nodes to be added to the networks during training process. Factor 3. complexity:- it can determine how hard the networks are built by constructive methods and is measured by number of weights or nodes. Factor 4. generalization ability:- it enables networks to avoid overfitting due to oversized network. In this thesis, the above four factors are considered when designing and implementing the newly proposed constructive approaches for a class of identification models, namely Wavelet Neural Networks (WNNs): 1. The Clustered Orthogonalized Residual Based Selection (CORBS) algorithm:- it fully utilizes characteristics of wavelet function (Factor 1) and a heuristic filtering parameter (Factor 2), thus trimming down the complexity (Factor 3) in training process; 2. A pruning algorithm for WNNs:- it automates the CORBS algorithm to acquire significant nodes and get optimum size for WNNs by fixing the heuristic filtering parameter (Factor 2) in the CORBS algorithm, resulting in enhancing the WNNs’ generalization ability (Factor 4); 3. The Dynamic FuzzyWavelet Networks (DFWNs) and their corresponding constructive approach:- they take advantages of combining the lowlevel learning and computational power of neural networks into fuzzy systems. On the other hand, high-level humanlike IF-THEN rule thinking and reasoning of fuzzy systems is introduced into neural networks. Together with the above advantages, the use of CORBS algorithm to construct the DFWNs enables the DFWNs to be fine-tuned dynamically by setting dynamic fuzzy rules (Factor 2) and fully utilizes characteristics of wavelet function (Factor 1). Finally, the above approaches are applied to several numerical examples. From the numerical examples, the new approaches are shown to have a better performance, as compared with other existing algorithms. To further understand the approaches, their stability and complexity as well as the characteristics of wavelet function are also analyzed in the examples.
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