A performance analysis of ForeNet on time series prediction.

• Other Authors: Lam, Hei Tat.
• Format: Others
• Language: English; Chinese
• Published: 2009
• Subjects: Neural networks (Computer science) > Mathematical models; Time-series analysis > Mathematical models
• Online Access: http://library.cuhk.edu.hk/record=b5894001; http://repository.lib.cuhk.edu.hk/en/item/cuhk-326718

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