| Foreword |
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vii | |
| Acknowledgements |
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xiii | |
| PART I INTRODUCTION TO WAVELET THEORY |
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1 | (30) |
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Introduction to Wavelet Theory |
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3 | (28) |
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A short overview on the development of wavelet theory |
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3 | (3) |
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Wavelet transform versus Fourier transform |
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6 | (7) |
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6 | (2) |
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Continuous Fourier transform |
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8 | (1) |
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Short-time Fourier transform versus wavelet transform |
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8 | (2) |
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Discrete wavelet decomposition |
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10 | (2) |
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Continuous wavelet transform |
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12 | (1) |
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The fast wavelet transform |
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13 | (7) |
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The dilation equations (or two-scales relations) |
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14 | (2) |
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Decomposition and reconstruction algorithms |
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16 | (4) |
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Definition of a Multiresolution |
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20 | (1) |
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21 | (2) |
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Wavelets and subband coding |
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23 | (3) |
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26 | (5) |
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26 | (1) |
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27 | (1) |
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28 | (3) |
| PART II PREPROCESSING: THE MULTIRESOLUTION APPROACH |
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31 | (40) |
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Preprocessing: The Multiresolution Approach |
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33 | (38) |
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The double curse: dimensionality and complexity |
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34 | (3) |
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35 | (1) |
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Classification of problems' difficulty |
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36 | (1) |
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37 | (6) |
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Karhunen-Loeve transform (principal components analysis) |
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38 | (2) |
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Search for good data representation with multiresolution principal components analysis |
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40 | (2) |
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Projection pursuit regression |
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42 | (1) |
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Exploratory projection pursuit |
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42 | (1) |
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Dimension reduction through wavelets-based projection methods |
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43 | (5) |
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43 | (4) |
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47 | (1) |
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Exploratory knowledge extraction |
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48 | (4) |
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Detecting nonlinear variables interactions with Haar wavelet trees |
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49 | (1) |
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Discovering non-significant variables with multiresolution techniques |
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50 | (2) |
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Wavelets in classification |
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52 | (5) |
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Classification with local discriminant basis selection algorithms |
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53 | (2) |
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Classification and regression trees (CART) with local discriminant basis selection algorithm preprocessing |
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55 | (2) |
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Applications of multiresolution techniques for preprocessing in soft computing |
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57 | (3) |
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57 | (2) |
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59 | (1) |
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59 | (1) |
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Application of multiresolution and fuzzy logic to fire detection |
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60 | (11) |
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61 | (3) |
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64 | (7) |
| PART III SPLINE-BASED WAVELETS APPROXIMATION AND COMPRESSION ALGORITHMS |
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71 | (20) |
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Spline-Based Wavelets Approximation and Compression Algorithms |
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73 | (18) |
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73 | (10) |
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Introduction to B-splines |
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73 | (3) |
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Biorthogonal spline-wavelet |
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76 | (3) |
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Semi-orthogonal B-wavelets |
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79 | (3) |
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82 | (1) |
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A selection of wavelet-based alrogithms for spline approximation |
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83 | (8) |
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83 | (3) |
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Thresholding adapted to the decomposition with scaling functions |
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86 | (2) |
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Matching pursuit with scaling functions |
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88 | (3) |
| PART IV ATUOMATIC GENERATION OF A FUZZY SYSTEM WITH WAVELET BASED METHODS |
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91 | (30) |
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Automatic Generation of a Fuzzy System with Wavelet-Based Methods |
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93 | (28) |
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93 | (8) |
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94 | (3) |
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97 | (1) |
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98 | (1) |
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Fuzzification of the output in a Takagi-Sugeno model |
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99 | (2) |
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Neurofuzzy spline modeling |
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101 | (1) |
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101 | (12) |
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103 | (2) |
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Soft computing approach to fuzzy-wavelet transform |
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105 | (1) |
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106 | (1) |
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Linguistic interpretation of the rules |
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107 | (3) |
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110 | (1) |
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Off-line learning from irregularly spaced data |
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111 | (2) |
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113 | (1) |
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Interpolation and approximation methods |
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113 | (8) |
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114 | (1) |
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Multivariate approximation methods |
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115 | (6) |
| PART V ON-LINE LEARNING |
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121 | (18) |
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123 | (16) |
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Wavelet-based neural networks |
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124 | (5) |
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127 | (2) |
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Dyadic wavelet networks or wavenets |
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129 | (1) |
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130 | (9) |
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Learning with fuzzy wavenets |
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132 | (1) |
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Validation methods in fuzzy wavenets |
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133 | (2) |
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Learning with wavelet-based feedforward neural networks |
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135 | (1) |
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What are good candidates scaling and wavelet functions at high dimension? |
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136 | (3) |
| PART VI NONPARAMETRIC WAVELET-BASED ESTIMATION AND REGRESSION TECHNIQUES |
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139 | (14) |
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Nonparametric Wavelet-Based Estimation and Regression Techniques |
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141 | (12) |
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Nonparametric regression and estimation techniques |
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141 | (2) |
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143 | (1) |
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144 | (4) |
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Wavelet methods for curve estimation |
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144 | (1) |
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Biorthogonal wavelet estimators |
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145 | (1) |
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146 | (1) |
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Wavelet denoising methods |
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146 | (2) |
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148 | (5) |
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Fuzzy wavelet estimators within the framework of the singleton model |
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148 | (2) |
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Multiresolution fuzzy wavelet estimators: application to on-line learning |
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150 | (1) |
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A probabilistic approach to fuzzy-wavelet |
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151 | (2) |
| PART VII DEVELOPING INTELLIGENT PRODUCTS |
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153 | (12) |
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Developing Intelligent Products |
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155 | (10) |
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155 | (3) |
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Man, sensors and computer intelligence |
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158 | (4) |
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162 | (3) |
| PART VIII GENETIC ALGORITHMS AND MULTIRESOLUTION |
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165 | (30) |
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The standard genetic algorithm |
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167 | (28) |
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Walsh functions and genetic algorithms |
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169 | (5) |
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169 | (2) |
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An alternative description of the Walsh functions using the formalism of wavelet packets |
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171 | (2) |
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On deceptive functions in genetic algorithms |
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173 | (1) |
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Wavelet-based genetic algorithms |
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174 | (16) |
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The wavelet-based genetic algorithm in the Haar wavelet formalism |
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176 | (3) |
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Connection between the wavelet-based genetic algorithm and filter theory |
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179 | (4) |
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Population evolution and deceptive functions |
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183 | (7) |
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190 | (5) |
| ANNEXES LIFTING SCHEME, NONLINEAR WAVELETS |
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195 | (14) |
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197 | (12) |
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197 | (2) |
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Biorthogonal spline-wavelets constructions with the lifting scheme |
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199 | (4) |
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203 | (1) |
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Said and Pearlman wavelets |
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203 | (1) |
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Morphological Haar wavelets |
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204 | (1) |
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Wavelets constructions for genetic algorithms |
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205 | (4) |
| References |
|
209 | (12) |
| Index |
|
221 | |
