This book presents the state of integration of wavelet theory and multiresolution analysis into soft computing. It is the first book on hybrid methods combining wavelet analysis with fuzzy logic, neural networks or genetic algorithms. Much attention is given to new approaches (fuzzy-wavelet) that permit one to develop, using wavelet techniques, linguistically interpretable fuzzy systems from data. The book also introduces the reader to wavelet-based genetic algorithms and multiresolution search. A special place is given to methods that have been implemented in real world applications, particularly the different techniques combining fuzzy logic or neural networks with wavelet theory.
Author(s): Marc Thuillard
Publisher: World Scientific Pub Co Inc
Year: 2001
Language: English
Pages: 246
Tags: Математика;Математическая логика;Нечеткая логика;
Foreword ......Page 8
Contents ......Page 14
Acknowledgements ......Page 20
Part I Introduction To Wavelet Theory ......Page 21
A short overview on the development of wavelet theory ......Page 23
Wavelet transform versus Fourier transform ......Page 26
The fast wavelet transform ......Page 33
Definition of a Multiresolution ......Page 40
Biorthogonal wavelets ......Page 41
Wavelets and subband coding ......Page 43
Applications ......Page 46
Part II Preprocessing: The Multiresolution Approach ......Page 51
2. Preprocessing: The Multiresolution Approach ......Page 53
The double curse: dimensionality and complexity ......Page 54
Dimension reduction ......Page 57
Dimension reduction through wavelets-based projection methods ......Page 63
Exploratory knowledge extraction ......Page 68
Wavelets in classification ......Page 72
Applications of multiresolution techniques for preprocessing in soft computing ......Page 77
Application of multiresolution and fuzzy logic to fire detection ......Page 80
Part III Spline-Based Wavelets Approximation And Compression Algorithms ......Page 91
Spline-based wavelets ......Page 93
A selection of wavelet-based alrogithms for spline approximation ......Page 103
Part IV Automatic Generation Of A Fuzzy System With Wavelet Based Methods ......Page 111
Fuzzy rule-based systems ......Page 113
Fuzzy-wavelet ......Page 121
Interpolation and approximation methods ......Page 133
Part V On-Line Learning ......Page 141
5. On-Line Learning ......Page 143
Wavelet-based neural networks ......Page 144
Dyadic wavelet networks or wavenets ......Page 149
Fuzzy wavenets ......Page 150
Part VI Nonparametric Wavelet-Based Estimation And Regression Techniques ......Page 159
Nonparametric regression and estimation techniques ......Page 161
Smoothing splines ......Page 163
Wavelet estimators ......Page 164
Fuzzy wavelet estimators ......Page 168
Part VII Developing Intelligent Products ......Page 173
Transparency ......Page 175
Man sensors and computer intelligence ......Page 178
Constructive modeling ......Page 182
Part VIII Genetic Algorithms And Multiresolution ......Page 185
8. The standard genetic algorithm ......Page 187
Walsh functions and genetic algorithms ......Page 189
Wavelet-based genetic algorithms ......Page 194
Multiresolution search ......Page 210
Annexes Lifting Scheme Nonlinear Wavelets ......Page 215
Lifting Scheme ......Page 217
Nonlinear wavelets ......Page 223
References ......Page 229
Index ......Page 241
