Wavelets in Soft Computing (Second Edition)

✍ Scribed by Marc Thuillard

• Publisher: World Scientific Publishing Co. Pte. Ltd.
• Year: 2023
• Tongue: English
• Leaves: 320
• Series: orld Scientific Series in Robotics and Intelligent Systems
• Edition: 2
• Category: Library

✦ Synopsis

The comprehensive compendium furnishes a quick and efficient entry point to many multiresolution techniques and facilitates the transition from an idea into a real project. It focuses on methods combining several soft computing techniques (fuzzy logic, neural networks, genetic algorithms) in a multiresolution framework. Illustrated with numerous vivid examples, this useful volume gives the reader the necessary theoretical background to decide which methods suit his/her needs. New materials and applications for multiresolution analysis are added, including notable research topics such as Deep Learning, graphs, and network analysis. Many Deep Learning applications incorporate a wavelet decomposition stage to better capture features at different resolutions, a quite sensible step as the size of an object in an image may greatly vary. A fascinating aspect that we discuss in a new chapter is that multiresolution is at the heart of the functioning of Deep Learning. Neural networks on graphs are important in studying communication networks and analyzing internet data. Here also, multiresolution permits a better analysis. The research community has broadly integrated the idea that the integration of multiresolution often improves algorithms. This new edition aims to capture some of these exciting new developments. Readership: Researchers, professionals, academics and graduate students in fuzzy logic.

✦ Table of Contents

Cover Page
Title Page
Copyright Page
Dedication
Foreword
Introduction to the Second Edition
Contents
Part 1 Introduction to Wavelet Theory
Chapter 1 Introduction to Wavelet Theory
1.1. A short overview of the development of wavelet theory
1.2. Wavelet transform versus Fourier transform
1.2.1. Fourier series
1.2.2. Continuous Fourier transform
1.2.3. Short-time Fourier transform versus wavelet transform
1.2.4. Discrete wavelet decomposition
1.2.5. Continuous wavelet transform
1.3. The fast wavelet transform
1.3.1. The dilation equations (or two-scales relations)
1.3.2. Decomposition and reconstruction algorithms
1.4. Definition of a multiresolution
1.5. Biorthogonal wavelets
1.6. Wavelets and subband coding
1.7. Contourlets and shearlet
1.7.1. Wavelet scattering technique
1.8. Empirical wavelet decomposition
1.8.1. Wavelet cross-correlation and coherence analysis
1.9. Applications
1.9.1. Data analysis
1.9.2. Data compression
1.9.3. Denoising
1.9.4. Super-resolution
1.10. Super-resolutionRecent applications of wavelet and multiresolution analysis
1.10.1. Applications of the Continuous Wavelet Transform (CWT)
1.10.2. Fluid dynamics applications of wavelets
References
Part 2 Preprocessing: The Multiresolution Approach
Chapter 2 Preprocessing: The Multiresolution Approach
2.1. The double curse: dimensionality and complexity
2.1.1. Curse of dimensionality
2.1.2. Classification of problems’ difficulty
2.2. Dimension reduction
2.3. Karhunen-Loève transform (principal components analysis)
2.3.1. Search for good data representation with multiresolution principal components analysis
2.3.2. Projection pursuit regression
2.3.3. Exploratory projection pursuit
2.4. Dimension reduction through wavelet-based projection methods
2.4.1. Best basis
2.4.2. Matching pursuit
2.5. Exploratory knowledge extraction
2.5.1. Detecting nonlinear variables’ interactions with Haar wavelet trees
2.5.2. Discovering non-significant variables with multiresolution techniques
2.6. Wavelets in classification
2.6.1. Classification with local discriminant basis selection algorithms
2.6.2. Classification and regression trees (CART) with local discriminant basis selection algorithm preprocessing
2.7. Applications of multiresolution techniques for preprocessing in soft computing
2.7.1. Neural networks
2.7.2. Fuzzy logic
2.7.3. Genetic algorithms
References
Part 3 Spline-Based Wavelets Approximation and Compression Algorithms
Chapter 3 Spline-Based Wavelets Approximation and Compression Algorithms
3.1. Spline-based wavelets
3.1.1. Introduction to B-splines
3.1.2. Semi-orthogonal B-wavelets
3.1.3. Battle-Lemarié wavelets
3.2. A selection of wavelet-based algorithms for spline approximation
3.2.1. Wavelet thresholding
3.2.2. Thresholding in the spline-wavelet framework
3.2.3. Matching pursuit with scaling functions
References
Part 4 Automatic Generation of a Fuzzy System with Wavelet-Based Methods and Spline-Based Wavelets
Chapter 4 Automatic Generation of a Fuzzy System with Wavelet-Based Methods and Spline-Based Wavelets
4.1. Fuzzy rule-based systems
4.1.1. Max-min method (Mamdani)
4.1.2. Takagi-Sugeno model
4.1.3. The singleton model
4.1.4. Fuzzification of the output in a Takagi-Sugeno model
4.2. Type-2 Fuzzy systems
4.3. Interpolation, extrapolation, and approximation methods
4.3.1. Spline interpolants
4.3.2. Multivariate approximation methods
4.4. Fuzzy wavelet
4.4.1. General approach
4.5. Soft computing approach to fuzzy wavelet transform
4.5.1. Processing boundaries
4.5.2. Linguistic interpretation of the rules
4.5.3. Fuzzy wavelet classifier
4.5.4. Offline learning from irregularly spaced data
4.5.5. Missing data
References
Part 5 Nonparametric Wavelet-Based Estimation and Regression Techniques
Chapter 5 Nonparametric Wavelet-Based Estimation and Regression Techniques
5.1. Introduction
5.2. Smoothing splines
5.3. Wavelet estimators
5.4. Wavelet methods for curve estimation
5.4.1. Biorthogonal wavelet estimators
5.4.2. Density estimators
5.4.3. Wavelet denoising methods
5.5. Fuzzy wavelet estimators
5.5.1. Fuzzy wavelet estimators within the framework of the singleton model
5.5.2. Multiresolution fuzzy wavelet estimators: application to online learning
References
Part 6 Hybrid Neural Networks
Chapter 6 Hybrid Neural Networks
6.1. Neuro-Fuzzy modeling
6.1.1. Adaptive Neuro-Fuzzy Adaptive Systems (ANFIS)
6.1.2. Neuro-fuzzy spline modeling
6.2. Wavelet-based neural networks
6.2.1. Wavelet networks
6.3. Extreme learning machines
6.3.1. Wavelet kernel and Fuzzy wavelet ELM
6.4. Dyadic wavelet networks or wavenets
6.5. Wavelet-based fuzzy neural networks
6.5.1. Fuzzy wavelet networks
6.5.2. Fuzzy wavenets
6.5.3. Learning with fuzzy wavenets
6.5.3.1. Validation methods in fuzzy wavenets
6.5.4. Learning with wavelet-based feedforward neural networks
6.6. Applications of wavelet, fuzzy wavelet networks, and wavenets
References
Part 7 Multiresolution and Deep Neural Networks
Chapter 7 Multiresolution and Deep Neural Networks
7.1. Introduction
7.2. Convolutional Neural Networks (CNN) and multiresolution
7.3. Generative Adversarial Networks (GAN)
7.3.1. Other related architectures related to generative networks
7.3.1.1. Autoencoders
7.3.1.2. Transformer
7.3.1.3. Siamese networks
7.4. U-nets and multiresolution
7.5. Fuzzy logic in deep learning
7.5.1. Improving the interpretability of deep learning with neuro-fuzzy
7.5.2. Fuzzy layers deal with noisy data and uncertainty
7.5.3. Deep fuzzy clustering
References
Part 8 Developing Intelligent Sensors with Fuzzy Logic and Multiresolution Analysis
Chapter 8 Developing Intelligent Sensors with Fuzzy Logic and Multiresolution Analysis
8.1. Application of multiresolution and fuzzy logic to fire detection
8.1.1. Linear beam detector
8.1.2. Flame detector
8.2. Transparency
8.3. Man, sensors, and computer intelligence
8.3.1. Local model failure
8.4. Constructive modeling
8.5. From a sensor to a smart sensor network with multicriteria decisions
References
Part 9 Multiresolution and Wavelets in Graphs, Trees, and Networks
Chapter 9 Multiresolution and Wavelets in Graphs, Trees, and Networks
9.1. Wavelet decomposition on a graph
9.1.1. Fourier and wavelet transforms on graphs
9.1.2. Graph wavelet neural networks
9.1.3. Spectral ordering
9.2. Treelet
9.3. Phylogenetic trees and networks
9.3.1. Effect of lateral transfers on phylogenetic trees and networks
9.3.2. Constructing a phylogenetic tree and outerplanar network from data
9.4. Multiresolution approach to phylogeny
9.4.1. Finding the best phylogenetic network
9.4.2. Clustering noisy data with NeighborNet
9.4.3. Automatic identification of simple instances of lateral transfer
9.5. Applications to phylogeography
9.5.1. Application on the classification of myths’ motifs
9.6. Continuous characters: Classification of galaxies
9.7. Outlook
References
Part 10 Genetic Algorithms and Multiresolution
Chapter 10 Genetic Algorithms and Multiresolution
10.1. The standard genetic algorithm
10.2. Walsh functions and genetic algorithms
10.2.1. Walsh functions
10.2.2. An alternative description of the Walsh functions using the formalism of wavelet packets
10.2.3. On deceptive functions in genetic algorithms
10.3. Wavelet-based genetic algorithms
10.3.1. The wavelet-based genetic algorithm in the Haar wavelet formalism
10.3.2. The connection between the wavelet-based genetic algorithm and filter theory
10.4. Population evolution and deceptive functions
10.5. Multiresolution search
10.6. Searching for a good solution: How to beat brute force
10.7. Swarm intelligence
References
Annexes
Annex A: Lifting scheme
Introduction
Biorthogonal spline-wavelets constructions with the lifting scheme
Annex B: Nonlinear wavelets
Said and Pearlman wavelets
Morphological Haar wavelets
Annex C: Phylogenetic trees and networks (Outerplanar Networks)
References
Index