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E-raamat: Adaptive Learning Methods for Nonlinear System Modeling

Edited by (Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, USA), Edited by (Department of Information Engineering, Electronics and Telecommunications - Sapienza University of Rome, Italy)
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  • Ilmumisaeg: 11-Jun-2018
  • Kirjastus: Butterworth-Heinemann Inc
  • Keel: eng
  • ISBN-13: 9780128129777
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Adaptive Learning Methods for Nonlinear System ModelingSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 11-Jun-2018
  • Kirjastus: Butterworth-Heinemann Inc
  • Keel: eng
  • ISBN-13: 9780128129777
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Adaptive Learning Methods for Nonlinear System Modeling presents some of the recent advances on adaptive algorithms and machine learning methods designed for nonlinear system modeling and identification. Real-life problems always entail a certain degree of nonlinearity, which makes linear models a non-optimal choice. This book mainly focuses on those methodologies for nonlinear modeling that involve any adaptive learning approaches to process data coming from an unknown nonlinear system. By learning from available data, such methods aim at estimating the nonlinearity introduced by the unknown system. In particular, the methods presented in this book are based on online learning approaches, which process the data example-by-example and allow to model even complex nonlinearities, e.g., showing time-varying and dynamic behaviors. Possible fields of applications of such algorithms includes distributed sensor networks, wireless communications, channel identification, predictive maintenance, wind prediction, network security, vehicular networks, active noise control, information forensics and security, tracking control in mobile robots, power systems, and nonlinear modeling in big data, among many others.

This book serves as a crucial resource for researchers, PhD and post-graduate students working in the areas of machine learning, signal processing, adaptive filtering, nonlinear control, system identification, cooperative systems, computational intelligence. This book may be also of interest to the industry market and practitioners working with a wide variety of nonlinear systems.

Arvustused

"This book is a joint work of an excellent international team of scientists working in the field of nonlinear signal processing and, in particular, designing adaptive filtering algorithms utilized in system identification and nonlinear system modeling."--Mathematical Reviews Clippings

Preface xvii
Acknowledgments xix
Chapter 1 Introduction
1(14)
1.1 Nonlinear System Modeling: Background, Motivation and Opportunities
1(3)
1.1.1 Modeling an Unknown System
1(1)
1.1.2 Suitable Models for Real-World Problems
2(1)
1.1.3 Challenges and Opportunities in Investigating Nonlinear Models
3(1)
1.2 Key Factors in Denning Adaptive Learning Methods for Nonlinear System Modeling
4(1)
1.3 Book Organization
5(4)
1.4 Further Readings
9(6)
References
9(6)
PART 1 LINEAR-IN-THE-PARAMETERS NONLINEAR FILTERS
Chapter 2 Orthogonal LIP Nonlinear Filters
15(32)
2.1 Introduction
16(3)
2.2 LIP Nonlinear Filters
19(13)
2.2.1 Nonlinear Filters and Stone-Weierstrass Theorem
19(1)
2.2.2 The Volterra and Wiener Theory
20(3)
2.2.3 FLiP Filters and Orthogonal FLiP Filters
23(8)
2.2.4 Simplified FLiP Filters
31(1)
2.3 Recent Identification Methods for Orthogonal Filters
32(7)
2.3.1 Perfect Periodic Sequences
33(5)
2.3.2 Multiple-Variance Methods
38(1)
2.4 Experimental Results
39(3)
2.4.1 Identification of Nonlinear Devices Using Perfect Periodic Sequences
39(2)
2.4.2 Multiple-Variance System Identification and Emulation
41(1)
2.5 Concluding Remarks
42(5)
References
43(4)
Chapter 3 Spline Adaptive Filters
47(24)
3.1 Introduction
48(1)
3.1.1 Notation
49(1)
3.2 Foundation of Spline Interpolation
49(3)
3.2.1 Uniform Cubic Spline
51(1)
3.3 Spline Adaptive Filters
52(5)
3.3.1 Wiener SAF
53(1)
3.3.2 Hammerstein SAF
54(1)
3.3.3 Sandwich 1 SAF
55(1)
3.3.4 Sandwich 2 SAF
55(1)
3.3.5 Other Architectures
56(1)
3.3.6 Computational Cost
57(1)
3.4 Convergence Properties
57(3)
3.4.1 Bounds on the Learning Rates
58(1)
3.4.2 Steady-State MSE
58(2)
3.5 Experimental Results
60(6)
3.5.1 Results From Simulated Scenarios
60(3)
3.5.2 Results From Real-World Scenarios
63(2)
3.5.3 Applicative Scenarios
65(1)
3.6 Conclusion
66(5)
Acknowledgments
66(1)
References
66(5)
Chapter 4 Recent Advances on LIP Nonlinear Filters and Their Applications
71(34)
4.1 Introduction
72(2)
4.2 A Concise Categorization of State-of-the-Art LIP Nonlinear Filters
74(3)
4.2.1 Hammerstein Models and Cascade Models
74(1)
4.2.2 Hammerstein Group Models and Cascade Group Models
75(1)
4.2.3 Bilinear Cascade Models
76(1)
4.3 Fundamental Methods for Coefficient Adaptation
77(9)
4.3.1 NLMS for Cascade Group Models
78(3)
4.3.2 Filtered-X Adaptation for Bilinear Cascade Models
81(4)
4.3.3 Summary of Algorithms
85(1)
4.4 Significance-Aware Filtering
86(7)
4.4.1 Significance-Aware Decompositions of LIP Nonlinear Systems
86(3)
4.4.2 Serial Significance-Aware Cascade Models
89(1)
4.4.3 Parallel Significance-Aware Cascade Group Models
90(2)
4.4.4 Parallel Significance-Aware Filtered-X Adaptation
92(1)
4.5 Experiments and Evaluation
93(4)
4.5.1 Evaluation Metrics
94(1)
4.5.2 Experiments
94(3)
4.6 Outlook on Model Structure Estimation
97(1)
4.7 Summary
98(7)
Acknowledgments
99(1)
References
99(6)
PART 2 ADAPTIVE ALGORITHMS IN THE REPRODUCING KERNEL HILBERT SPACE
Chapter 5 Maximum Correntropy Criterion-Based Kernel Adaptive Filters
105(22)
5.1 Introduction
106(1)
5.2 Kernel Adaptive Filters
107(2)
5.2.1 KLMS Algorithm
107(1)
5.2.2 KRLS Algorithm
107(2)
5.3 Maximum Correntropy Criterion
109(5)
5.3.1 Correntropy
109(3)
5.3.2 Maximum Correntropy Criterion
112(2)
5.4 Kernel Adaptive Filters Under Generalized MCC
114(5)
5.4.1 Generalized Kernel Maximum Correntropy
114(3)
5.4.2 Generalized Kernel Recursive Maximum Correntropy
117(2)
5.5 Simulation Results
119(5)
5.5.1 Frequency Doubling Problem
119(1)
5.5.2 Online Nonlinear System Identification
120(2)
5.5.3 Noise Cancellation
122(2)
5.6 Conclusion
124(3)
References
124(3)
Chapter 6 Kernel Subspace Learning for Pattern Classification
127(22)
6.1 Introduction
128(1)
6.2 Kernel Methods
129(5)
6.2.1 Notations
129(1)
6.2.2 Nonparametric Learning Model
130(1)
6.2.3 Training With Kernel Methods
130(2)
6.2.4 Model Complexity
132(1)
6.2.5 Kernel Approximation and Related Work
132(2)
6.3 Kernel Subspace Approximation
134(3)
6.3.1 Motivation
134(1)
6.3.2 Training Complexity With Approximation
135(2)
6.4 Adaptive Kernel Subspace Approximation Algorithm
137(4)
6.4.1 Algorithmic Framework
137(1)
6.4.2 Algorithm Design
137(4)
6.5 Infrastructures
141(4)
6.5.1 Speedup: GPU/CUDA
141(1)
6.5.2 Scaling: Spark
142(3)
6.6 Conclusion
145(4)
Appendix 6.A
145(1)
6.A.1 Centering
145(1)
6.A.2 Normalization
146(1)
References
146(3)
Chapter 7 A Random Fourier Features Perspective of KAFs With Application to Distributed Learning Over Networks
149(24)
7.1 Introduction
150(1)
7.2 Approximating the Kernel
151(1)
7.3 Online Kernel-Based Learning: A Random Fourier Features Perspective
152(9)
7.3.1 RFF-KLMS
152(3)
7.3.2 RFF-KRLS
155(1)
7.3.3 RFF-PEGASOS
155(2)
7.3.4 Simulations---Regression
157(1)
7.3.5 Simulations---Classification
157(4)
7.4 Online Distributed Learning With Kernels
161(9)
7.4.1 Diffusion KLMS
164(2)
7.4.2 Diffusion PEGASOS
166(2)
7.4.3 Simulations---Diffusion KLMS
168(1)
7.4.4 Simulations---Diffusion PEGASOS
168(2)
7.5 Conclusions
170(3)
References
171(2)
Chapter 8 Kernel-Based Inference of Functions Over Graphs
173(28)
8.1 Introduction
173(1)
8.2 Reconstruction of Functions Over Graphs
174(11)
8.2.1 Kernel Regression
175(2)
8.2.2 Kernels on Graphs
177(2)
8.2.3 Selecting Kernels From a Dictionary
179(2)
8.2.4 Semiparametric Reconstruction
181(2)
8.2.5 Numerical Tests
183(2)
8.3 Inference of Dynamic Functions Over Dynamic Graphs
185(16)
8.3.1 Kernels on Extended Graphs
186(4)
8.3.2 Multikernel Kriged Kalman Filters
190(3)
8.3.3 Numerical Tests
193(2)
8.3.4 Summary
195(1)
Acknowledgments
196(1)
References
196(5)
PART 3 NONLINEAR MODELING WITH MULTIPLE LEARNING MACHINES
Chapter 9 Online Nonlinear Modeling via Self-Organizing Trees
201(22)
9.1 Introduction
202(2)
9.2 Self-Organizing Trees for Regression Problems
204(5)
9.2.1 Notation
204(1)
9.2.2 Construction of the Algorithm
205(3)
9.2.3 Convergence of the Algorithm
208(1)
9.3 Self-Organizing Trees for Binary Classification Problems
209(4)
9.3.1 Construction of the Algorithm
209(3)
9.3.2 Convergence of the Algorithm
212(1)
9.4 Numerical Results
213(10)
9.4.1 Numerical Results for Regression Problems
213(4)
9.4.2 Numerical Results for Classification Problems
217(2)
Appendix 9.A
219(1)
9.A.1 Proof of Theorem 1
219(2)
9.A.2 Proof of Theorem 2
221(1)
Acknowledgments
221(1)
References
221(2)
Chapter 10 Adaptation and Learning Over Networks for Nonlinear System Modeling
223(20)
10.1 Introduction
224(1)
10.2 Mathematical Formulation of the Problem
225(5)
10.2.1 Problem Setup
226(1)
10.2.2 Diffusion-Based Algorithms
227(2)
10.2.3 Extension to Multitask Learning
229(1)
10.3 Existing Approaches to Nonlinear Distributed Filtering
230(5)
10.3.1 Expansion Over Random Bases
230(1)
10.3.2 Distributed Kernel Filters
231(2)
10.3.3 Diffusion Spline Filters
233(2)
10.4 A Distributed Kernel Filter for Multitask Problems
235(1)
10.5 Experimental Evaluation
236(2)
10.5.1 Experiment Setup
236(1)
10.5.2 Results and Discussion
237(1)
10.6 Discussion and Open Problems
238(2)
Acknowledgments
240(1)
References
240(3)
Chapter 11 Combined Filtering Architectures for Complex Nonlinear Systems
243(24)
11.1 Introduction
244(1)
11.2 Nonlinear Adaptive Filters
245(3)
11.2.1 Adaptive Volterra Filters
245(1)
11.2.2 Split Functional Link Adaptive Filters
246(1)
11.2.3 Kernel Adaptive Filters
247(1)
11.3 Different Approaches to Combine Nonlinear Adaptive Filters
248(3)
11.4 Combined Nonlinear Filters With Diversity in the Parameters
251(1)
11.5 Combination Schemes to Simplify the Selection of the Filter Structure
252(10)
11.5.1 Robust VFs for Nonlinear Acoustic Echo Cancellation
252(4)
11.5.2 Improved Multikernel Adaptive Filters With Selective Bias
256(6)
11.6 Conclusions
262(1)
References
263(4)
PART 4 NONLINEAR MODELING BY NEURAL SYSTEMS
Chapter 12 Echo State Networks for Multidimensional Data: Exploiting Noncircularity and Widely Linear Models
267(22)
12.1 Introduction
268(2)
12.2 Mathematical Background
270(4)
12.2.1 Quaternion Algebra
270(1)
12.2.2 Quaternion Widely Linear Model and Quaternion Augmented Statistics
271(1)
12.2.3 HM-Calculus and Quaternion Gradient Operations
272(1)
12.2.4 Quaternion Nonlinear Activation Functions
273(1)
12.3 Quaternion ESNs
274(7)
12.3.1 Standard QESNs
274(3)
12.3.2 Augmented QESNs
277(2)
12.3.3 Stability Analysis of QESNs and AQESNs
279(2)
12.4 Simulations
281(5)
12.5 Discussion and Conclusion
286(3)
Acknowledgments
286(1)
References
286(3)
Chapter 13 Identification of Short-Term and Long-Term Functional Synaptic Plasticity From Spiking Activities
289(24)
13.1 Introduction
290(2)
13.2 Identification of STSP With Nonlinear Dynamical Model
292(5)
13.2.1 Theory
292(3)
13.2.2 Nonlinear Dynamical Model of the Hippocampal CA3-CA1
295(2)
13.3 Identification of LTSP With Nonstationary Model
297(5)
13.3.1 Theory
297(1)
13.3.2 Simulation Studies on Nonstationary Nonlinear Dynamical Model
298(4)
13.4 Identification of Synaptic Learning Rule
302(6)
13.4.1 Theory
302(2)
13.4.2 Relationship Between Volterra Kernels and STDP
304(1)
13.4.3 Simulation Studies on Learning Rule Identification
304(4)
13.5 Summary and Discussion
308(5)
Acknowledgments
309(1)
References
309(4)
Chapter 14 Adaptive H∞ Tracking Control of Nonlinear Systems Using Reinforcement Learning
313(22)
14.1 Introduction
314(1)
14.2 Hoc Optimal Tracking Control for Nonlinear Affine Systems
315(7)
14.2.1 HJI Equation for H∞ Optimal Tracking
316(2)
14.2.2 Off-Policy IRL for Learning the Tracking HJI Equation
318(2)
14.2.3 Implementing Algorithm 2 Using Neural Networks
320(2)
14.3 Hoc Optimal Tracking Control for a Class of Nonlinear Nonaffine Systems
322(13)
14.3.1 A Class of Nonaffine Dynamical Systems
322(2)
14.3.2 Performance Function and H∞ Control Tracking for Nonaffine Systems
324(1)
14.3.3 Solution of the Control Tracking Problem of Nonaffine Systems
325(2)
14.3.4 Off-Policy Reinforcement Learning for Nonaffine Systems
327(3)
14.3.5 Neural Networks for Implementation of Off-Policy RL Algorithms
330(2)
References
332(3)
Chapter 15 Adaptive Dynamic Programming for Optimal Control of Nonlinear Distributed Parameter Systems
335(26)
15.1 Introduction
336(1)
15.2 Problem Description
337(1)
15.3 Model Reduction Based on KLD and Singular Perturbation Technique
338(2)
15.4 Adaptive Optimal Control Design With NDP
340(8)
15.4.1 Neurodynamic Programming
340(2)
15.4.2 Stability Analysis
342(3)
15.4.3 Simulation Studies
345(3)
15.5 Adaptive Optimal Control Based on Policy Iteration for Partially Unknown DPSs
348(8)
15.5.1 Policy Iteration
349(1)
15.5.2 Adaptive Optimal Control Based on Policy Iteration
350(1)
15.5.3 Implementation Procedure
351(1)
15.5.4 Stability Analysis
352(3)
15.5.5 Simulation Studies
355(1)
15.6 Conclusions
356(5)
Acknowledgments
357(1)
References
357(4)
Index 361
Danilo Comminiello is a Tenure-Track Assistant Professor with the Department of Information Engineering, Electronics and Telecommunications (DIET) at Sapienza University of Rome, Italy, where he teaches Machine Learning for Signal Processing. His current research interests include computational intelligence and machine learning theory, particularly focused on audio and acoustic applications. Danilo Comminiello is a Senior Member of Institute of Electrical and Electronics Engineers” (IEEE), and Member of Audio Engineering Society” (AES) and European Association for Signal Processing” (EURASIP). He is also a member of the Task Force on Computational Audio Processing” of the IEEE Intelligent System Applications” Technical Committee (IEEE Computational Intelligence Society). Jose C. Principe is a Distinguished Professor of Electrical and Computer Engineering and Biomedical Engineering at the University of Florida where he teaches advanced signal processing, machine learning and artificial neural networks (ANNs) modeling. He is BellSouth Professor and the Founding Director of the University of Florida Computational NeuroEngineering Laboratory (CNEL). His primary research interests are in advanced signal processing with information theoretic criteria (entropy and mutual information) and adaptive models in reproducing kernel Hilbert spaces (RKHS), and the application of these advanced algorithms to Brain Machine Interfaces (BMI). Dr. Principe is a Fellow of the IEEE, ABME, and AIBME. He is the past Editor in Chief of the IEEE Transactions on Biomedical Engineering, past Chair of the Technical Committee on Neural Networks of the IEEE Signal Processing Society, and Past-President of the International Neural Network Society. He received the IEEE EMBS Career Award, and the IEEE Neural Network Pioneer Award. He has more than 600 publications and 30 patents (awarded or filed).
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