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.
Contents:
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Foreword
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Introduction to the Second Edition
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Introduction to Wavelet Theory:
- A Short Overview of the Development of Wavelet Theory
- Wavelet Transform versus Fourier Transform
- The Fast Wavelet Transform
- Definition of a Multiresolution
- Biorthogonal Wavelets
- Wavelets and Subband Coding
- Contourlets and Shearlet
- Empirical Wavelet Decomposition
- Applications
- Recent Applications of Wavelet and Multiresolution Analysis
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Preprocessing: The Multiresolution Approach:
- The Double Curse: Dimensionality and Complexity
- Dimension Reduction
- Karhunen-Loeve Transform (Principal Components Analysis)
- Dimension Reduction Through Wavelet-Based Projection Methods
- Exploratory Knowledge Extraction
- Wavelets in Classification
- Applications of Multiresolution Techniques for Preprocessing in Soft Computing
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Spline-Based Wavelets Approximation and Compression Algorithms:
- Spline-Based Wavelets
- A Selection of Wavelet-Based Algorithms for Spline Approximation
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Automatic Generation of a Fuzzy System with Wavelet-Based Methods and Spline-Based Wavelets:
- Fuzzy Rule-Based Systems
- Type-2 Fuzzy Systems
- Interpolation, Extrapolation, and Approximation Methods
- Fuzzy Wavelet
- Soft Computing Approach to Fuzzy Wavelet Transform
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Nonparametric Wavelet-Based Estimation and Regression Techniques:
- Introduction
- Smoothing Splines
- Wavelet Estimators
- Wavelet Methods for Curve Estimation
- Fuzzy Wavelet Estimators
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Hybrid Neural Networks:
- Neuro-Fuzzy Modeling
- Wavelet-Based Neural Networks
- Extreme Learning Machines
- Dyadic Wavelet Networks Or Wavenets
- Wavelet-Based Fuzzy Neural Networks
- Applications of Wavelet, Fuzzy Wavelet Networks, and Wavenets
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Multiresolution and Deep Neural Networks:
- Introduction
- Convolutional Neural Networks (CNN) and Multiresolution
- Generative Adversarial Networks (GAN)
- U-Nets and Multiresolution
- Fuzzy Logic in Deep Learning
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Developing Intelligent Sensors with Fuzzy Logic and Multiresolution Analysis:
- Application of Multiresolution and Fuzzy Logic to Fire Detection
- Transparency
- Man, Sensors, and Computer Intelligence
- Constructive Modeling
- From a Sensor to a Smart Sensor Network with Multicriteria Decisions
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Multiresolution and Wavelets in Graphs, Trees, and Networks:
- Wavelet Decomposition on a Graph
- Treelet
- Phylogenetic Trees and Networks
- Multiresolution Approach to Phylogeny
- Applications to Phylogeography
- Continuous Characters: Classification of Galaxies
- Outlook
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Genetic Algorithms and Multiresolution:
- The Standard Genetic Algorithm
- Walsh Functions and Genetic Algorithms
- Wavelet-Based Genetic Algorithms
- Population Evolution and Deceptive Functions
- Multiresolution Search
- Searching for a Good Solution: How to Beat Brute Force
- Swarm Intelligence
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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)
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Index
Readership: Researchers, professionals, academics and graduate students in fuzzy logic.
