Mathematical Preliminaries / I: |
Sets / 1.1: |
Functions / 1.2: |
Sequences and Series / 1.3: |
Complex Numbers / 1.4: |
Linear Spaces / 1.5: |
Matrices / 1.6: |
Hilbert Spaces / 1.7: |
Topology / 1.8: |
Measure and Integral / 1.9: |
Fourier Series / 1.10: |
Exercises / 1.11: |
Wavelets / 2: |
Introduction / 2.1: |
Dilation and Translation / 2.2: |
Inner Product / 2.3: |
Haar Wavelet / 2.4: |
Multiresolution Analysis / 2.5: |
Continuous Wavelet Transform / 2.6: |
Discrete Wavelet Transform / 2.7: |
Fourier Transform / 2.8: |
Discrete Fourier Transform / 2.9: |
DFT of Finite Sequences / 2.10: |
Convolution / 2.11: |
Neural Networks / 2.12: |
McCulloch-Pitts Model of Neuron / 3.1: |
Optimal Network Structure / 3.1.2: |
Single Layer Perceptron / 3.1.3: |
Multilayer Perceptrons / 3.2: |
Adaptation Procedure of Rosenblatt / 3.2.1: |
Backpropagation Learning / 3.2.2: |
Hebbian Learning / 3.3: |
Hebb's Rule / 3.3.1: |
Hebbian Learning Applied to Multiple Input PEs / 3.3.2: |
Oja's Rule / 3.3.3: |
Sanger's Rule / 3.3.4: |
Principal Component Analysis (PCA) / 3.3.5: |
Anti-Hebbian Learning / 3.3.6: |
Competitive and Kohonen Networks / 3.4: |
Competitive Learning / 3.4.1: |
Kohonen Self-Organizing Map / 3.4.2: |
Grossberg's Instar-Outstar Network / 3.4.3: |
Adaptive Resonance Theory (ART) / 3.4.4: |
Recurrent Neural Networks / 3.5: |
Hopfield Networks / 3.5.1: |
Wavelet Networks / 3.6: |
What are Wavelet Networks? / 4.1: |
Dyadic Wavelet Network / 4.3: |
Theory of Wavelet Networks / 4.4: |
Wavelet Network Structure / 4.5: |
Wavelet Network Algorithm / 4.5.1: |
Multidimensional Wavelets / 4.6: |
Learning in Wavelet Networks / 4.7: |
Initialization of Wavelet Networks / 4.8: |
Properties of Wavelet Networks / 4.9: |
Scaling at Higher Dimensions |
Recurrent Learning / 4.11: |
Neural Structures / 5.1: |
Learning Problems / 5.2.2: |
On-line Learning Approaches: Recurrent Backpropagation / 5.2.3: |
Recurrent Wavelets / 5.3: |
Wavelets in Function Approximation / 5.3.1: |
Recurrent Wavelet Networks / 5.3.2: |
Numerical Experiments / 5.4: |
Case 1 / 5.4.1: |
Case 2 / 5.4.2: |
Concluding Remarks / 5.5: |
Separating Order from Disorder / 5.6: |
Order within Disorder / 6.1: |
Wavelet Networks: Trading Advisors / 6.2: |
Comparison Results / 6.3: |
Conclusions / 6.4: |
Radial Wavelet Neural Networks / 6.5: |
Data Description and Preparation / 7.1: |
Classification Systems / 7.3: |
Minimum Distance Classifier / 7.3.1: |
Wavelet Neural Network Classifier / 7.3.2: |
Results / 7.4: |
Predicting Chaotic Time Series / 7.5: |
Nonlinear Prediction / 8.1: |
Short-Term Prediction / 8.3: |
Parameter-Varying Systems / 8.5: |
Long-Term Prediction / 8.6: |
Appendix / 8.7: |
Acknowledgments / 8.9: |
Figures / 8.10: |
Concept Learning / 8.11: |
Background / 9.1: |
Preliminaries / 9.2: |
PAC Learning / 9.3.1: |
Approximation by Wavelet Networks / 9.3.2: |
Stochastic Approximation Algorithms / 9.3.3: |
Learning Algorithms / 9.4: |
Basic Algorithm / 9.4.1: |
Batching Algorithm / 9.4.2: |
Summary / 9.5: |
Bibliography / 9.6: |
Index / 10.1: |
Mathematical Preliminaries / I: |
Sets / 1.1: |
Functions / 1.2: |
Sequences and Series / 1.3: |
Complex Numbers / 1.4: |
Linear Spaces / 1.5: |