Foundations of Wavelet Networks and Applications Book

1	Mathematical Preliminaries	3
	Sets	3
	Functions	7
	Sequences and Series	11
	Complex Numbers	14
	Linear Spaces	17
	Matrices	23
	Hilbert Spaces	27
	Topology	29
	Measure and Integral	31
	Fourier Series	33
2	Wavelets	41
	Dilation and Translation	43
	Inner Product	44
	Haar Wavelet	45
	Multiresolution Analysis	47
	Continuous Wavelet Transform	49
	Discrete Wavelet Transform	52
	Fourier Transform	53
	Discrete Fourier Transform	55
	DFT of Finite Sequences	56
	Convolution	57
3	Neural Networks	61
	Multilayer Perceptrons	70
	Hebbian Learning	75
	Competitive and Kohonen Networks	84
	Recurrent Neural Networks	95
4	Wavelet Networks	107
	What are Wavelet Networks?	110
	Dyadic Wavelet Network	112
	Theory of Wavelet Networks	113
	Wavelet Network Structure	115
	Multidimensional Wavelets	120
	Learning in Wavelet Networks	121
	Initialization of Wavelet Networks	121
	Properties of Wavelet Networks	122
	Scaling at Higher Dimensions	123
5	Recurrent Learning	129
	Recurrent Neural Networks	130
	Recurrent Wavelets	136
	Numerical Experiments	142
	Concluding Remarks	143
6	Separating Order from Disorder	145
	Order within Disorder	145
	Wavelet Networks: Trading Advisors	148
	Comparison Results	149
7	Radial Wavelet Neural Networks	155
	Data Description and Preparation	156
	Classification Systems	158
	Results	165
8	Predicting Chaotic Time Series	171
	Nonlinear Prediction	176
	Wavelet Networks	177
	Short-Term Prediction	180
	Parameter-Varying Systems	183
	Long-Term Prediction	185
9	Concept Learning	205
	Preliminaries	207
	Learning Algorithms	212
10	Bibliography	223
	Mathematical Preliminaries	225
	Wavelets	225
	Neural Networks	226
	Wavelet Networks	235
	Recurrent Learning	240
	Separating Order from Disorder	244
	Radial Wavelet Neural Networks	244
	Predicting Chaotic Time Series	245
	Concept Learning	248
	Index	254