Lam, Hei Tat. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 124-131). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Time Series Prediction and Neural Networks --- p.1 / Chapter 1.2 --- ForeNet --- p.2 / Chapter 1.3 --- Objective and Motivation --- p.3 / Chapter 1.4 --- Organization of Chapters --- p.4 / Chapter 2 --- Background --- p.5 / Chapter 2.1 --- Neural Network Models for Temporal Data --- p.5 / Chapter 2.1.1 --- Representation of Temporal Information --- p.6 / Chapter 2.1.2 --- Elman Networks --- p.7 / Chapter 2.1.3 --- Real Time Recurrent Learning --- p.8 / Chapter 2.2 --- Recent Neural Networks Models --- p.10 / Chapter 2.2.1 --- Complex-valued Neural Networks --- p.11 / Chapter 2.2.2 --- Neural Networks working in Frequency Domain --- p.12 / Chapter 2.3 --- ForeNet Model --- p.13 / Chapter 2.3.1 --- Fourier Analysis of Time Series --- p.13 / Chapter 2.3.2 --- Recursive Prediction Equations --- p.14 / Chapter 2.3.3 --- Neural Network Representation --- p.16 / Chapter 2.3.4 --- Limitations of ForeNet --- p.19 / Chapter 3 --- Analysis of ForeNet --- p.20 / Chapter 3.1 --- Analysis of Single Neuron Response --- p.20 / Chapter 3.1.1 --- General Input --- p.21 / Chapter 3.1.2 --- Constant Input --- p.22 / Chapter 3.1.3 --- Sinusoidal Input --- p.27 / Chapter 3.2 --- Analysis of Network Response --- p.34 / Chapter 3.2.1 --- Network response function for Sinusoidal Input --- p.34 / Chapter 3.2.2 --- General Response Function for ForeNet --- p.39 / Chapter 3.3 --- Properties of ForeNet --- p.39 / Chapter 3.3.1 --- Desired Properties --- p.40 / Chapter 3.3.2 --- Magnitude of Output --- p.41 / Chapter 3.3.3 --- Phase of Output --- p.43 / Chapter 3.3.4 --- Output Magnitude Correction --- p.44 / Chapter 3.3.5 --- Operating Frequency Range --- p.45 / Chapter 3.3.6 --- Symmetry of Hidden Neurons --- p.47 / Chapter 3.4 --- Analysis of Simulation Error --- p.48 / Chapter 3.5 --- Chapter Summary --- p.53 / Chapter 4 --- Multi-parameterized Model --- p.54 / Chapter 4.1 --- Network Model --- p.54 / Chapter 4.1.1 --- Modified Recursive Prediction Equation --- p.54 / Chapter 4.1.2 --- Complex-valued Recurrent Network Model --- p.56 / Chapter 4.1.3 --- Network Initialization --- p.58 / Chapter 4.2 --- Analysis of Parameters --- p.60 / Chapter 4.2.1 --- Analysis of Network Response --- p.60 / Chapter 4.2.2 --- Effect of Decay Factor --- p.62 / Chapter 4.2.3 --- Effect of Neuron Natural Frequency --- p.66 / Chapter 4.2.4 --- Operating Frequency Range --- p.66 / Chapter 4.3 --- Experiment on Single Neuron --- p.68 / Chapter 4.4 --- Experiment on Two Neuron Model --- p.70 / Chapter 4.4.1 --- Single Input Frequency --- p.70 / Chapter 4.4.2 --- Random Multiple Input Frequencies --- p.72 / Chapter 4.5 --- Experiment of Comparisons to ForeNet --- p.74 / Chapter 4.6 --- Chapter Summary --- p.76 / Chapter 5 --- Training ForeNet --- p.78 / Chapter 5.1 --- Complex Real Time Recurrent Learning --- p.78 / Chapter 5.1.1 --- Learning of Output Weights --- p.80 / Chapter 5.1.2 --- Learning of Input and Recurrent Hidden Weights --- p.82 / Chapter 5.1.3 --- Evaluation of Complex Sensitivity Terms --- p.85 / Chapter 5.1.4 --- Summary of Learning Rules for Multi-parameterized ForeNet --- p.87 / Chapter 5.1.5 --- Computational Complexity --- p.89 / Chapter 5.2 --- Experiment on Convergence of Error --- p.89 / Chapter 5.3 --- Experiment of Data with Mixed Frequency --- p.92 / Chapter 5.4 --- Experiment of Various Time Series --- p.98 / Chapter 5.4.1 --- Experiment Setting --- p.98 / Chapter 5.4.2 --- Time Series --- p.99 / Chapter 5.4.3 --- Experimental Result --- p.104 / Chapter 5.4.4 --- Analysis on Initial and Final Error --- p.104 / Chapter 5.4.5 --- Analysis on Convergency --- p.109 / Chapter 5.5 --- Chapter Summary --- p.111 / Chapter 6 --- Discussion and Conclusion --- p.113 / Chapter 6.1 --- ForeNet as a Non-recursive Response Function --- p.113 / Chapter 6.2 --- Analysis in Frequency Domain --- p.114 / Chapter 6.2.1 --- Another View of ForeNet Model --- p.115 / Chapter 6.2.2 --- Linearity in Frequency Domain --- p.116 / Chapter 6.2.3 --- Direct Estimation of Error --- p.116 / Chapter 6.2.4 --- Analytic Solution to p-steps Ahead Prediction --- p.117 / Chapter 6.2.5 --- Providing Insights to Further Extension --- p.118 / Chapter 6.3 --- Performance Evaluation --- p.119 / Chapter 6.3.1 --- Performance Measurement --- p.119 / Chapter 6.3.2 --- Time Series Used --- p.121 / Chapter 6.4 --- Conclusion: Multi-parameterized ForeNet and its frequency recommendation --- p.122 / Bibliography --- p.124
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326718 |
| Date | January 2009 |
| Contributors | Lam, Hei Tat., Chinese University of Hong Kong Graduate School. Division of Computer Science and Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, xiii, 131 p. : ill. (some col.) ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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