Kernel Mode Decomposition and the Programming of Kernels (Surveys and Tutorials in the Applied Mathematical Sciences)

Preface
Acknowledgments
Contents
1 Introduction
	1.1 The Empirical Mode Decomposition Problem
	1.2 Programming Kernels Through Regression Networks and Kernel Mode Decomposition
	1.3 Mode Decomposition with Unknown Waveforms
	1.4 Structure of the Monograph
2 Review
	2.1 Additive Gaussian Processes
	2.2 Gaussian Process Regression
	2.3 Empirical Mode Decomposition (EMD)
	2.4 Synchrosqueezing
3 The Mode Decomposition Problem
	3.1 Optimal Recovery Setting
	3.2 Game/Decision Theoretic Setting
	3.3 Gaussian Process Regression Setting
4 Kernel Mode Decomposition Networks (KMDNets)
	4.1 Model/Data Alignment and Energy/Variance Decomposition
	4.2 Programming Modules and Feedforward Network
	4.3 Hierarchical Mode Decomposition
	4.4 Mode Decomposition Through Partitioning and Integration
	4.5 Application to Time–Frequency Decomposition
	4.6 Convergence of the Numerical Methods
5 Additional Programming Modules and Squeezing
	5.1 Elementary Programming Modules
	5.2 Programming the Network
	5.3 Alignments Calculated in L2
	5.4 Squeezing
	5.5 Crossing Instantaneous Frequencies
6 Non-trigonometric Waveform and Iterated KMD
	6.1 The Micro-Local KMD Module
	6.2 The Lowest Instantaneous Frequency
	6.3 The Iterated Micro-Local KMD Algorithm
	6.4 Numerical Experiments
		6.4.1 Triangle Wave Example
		6.4.2 EKG Wave Example
7 Unknown Base Waveforms
	7.0.1 Micro-Local Waveform KMD
	7.0.2 Iterated Micro-Local KMD with Unknown Waveforms Algorithm
	7.1 Numerical Experiments
8 Crossing Frequencies, Vanishing Modes, and Noise
	8.1 Illustrative Examples
	8.2 Identifying Modes and Segments
	8.3 The Segmented Micro-Local KMD Algorithm
	8.4 Numerical Experiments
Appendix
	9.1 Universality of the Aggregated Kernel
		9.1.1 Characterizing the Norm n=-NNe-|n|α22|cn|2
	9.2 Proofs
		9.2.1 Proof of Lemma 3.1.1
		9.2.2 Proof of Lemma 3.1.2
		9.2.3 Proof of Theorem 3.1.3
		9.2.4 Proof of Theorem 3.1.4
		9.2.5 Proof of Proposition 4.1.1
		9.2.6 Proof of Theorem 4.3.3
		9.2.7 Proof of Theorem 4.3.5
		9.2.8  Proof of Theorem 5.3.1
		9.2.9 Proof of Lemma 9.1.1
		9.2.10 Proof of Lemma 9.1.2
Bibliography
Index