 |
Correlative learning : a basis for brain and adaptive systems / Zhe Chen ... [et al.]. — Hoboken, N.J. : Wiley-Interscience, c2007. – (59.59785/C824) |
Contents
CONTENTS
Foreword
Preface
Acknowledgments
Acronyms
Introduction
1 THE CORRELATIVE BRAIN
1.1 Background / 8
1.2 Correlation Detection in Single Neurons / 19
1.3 Correlation in Ensembles of Neurons: Synchrony and Population Coding / 25
1.4 Correlation is the Basis of Novelty Detection and Learning / 31
1.5 Correlation in Sensory Systems: Coding， Perception， and Development / 38
1.6 Correlation in Memory Systems / 47
1.7 Correlation in Sensorimotor Learning / 52
1.8 Correlation， Feature Binding， and Attention / 57
1.9 Correlation and Cortical Map Changes after Peripheral Lesions and Brain Stimulation / 59
1.10 Discussion / 67
2 Correlation in Signal Processing 72
2.1 Correlation and Spectrum Analysis / 73
2.2 Wiener Filter / 91
2.3 Least-Mean-Square Filter / 95
2.4 Recursive Least-Squares Filter / 99
2.5 Matched Filter / 100
2.6 Higher Order Correlation-Based Filtering / 102
2.7 Correlation Detector / 104
2.8 Correlation Method for Time-Delay Estimation / 108
2.9 Correlation-Based Statistical Analysis / 110
2.10 Discussion / 122
Appendix 2A: Eigenanalysis of Autocorrelation Function of Nonstationary Process / 122
Appendix 2B: Estimation of Intensity and Correlation Functions of Stationary Random Point Process / 123
Appendix 2C: Derivation of Learning Rules with Quasi-Newton Method / 125
3 correlation-based neural learning and machine learning 129
3.1 Correlation as a Mathematical Basis for Learning / 130
3.2 Information-Theoretic Learning / 158
3.3 Correlation-Based Computational Neural Models / 182
Appendix 3A: Mathematical Analysis of Hebbian Learning* / 208
Appendix 3B: Necessity and Convergence of Anti-Hebbian Learning / 209
Appendix 3C: Link between Hebbian Rule and Gradient Descent / 210
Appendix 3D: Reconstruction Error in Linear and Quadratic PCA / 211
4 Correlation-Based Kernel Learning 218
4.1 Background / 218
4.2 Kernel PCA and Kernelized GHA / 221
4.3 Kernel CCA and Kernel ICA / 225
4.4 Kernel Principal Angles / 230
4.5 Kernel Discriminant Analysis / 232
4.6 Kernel Wiener Filter / 235
4.7 Kernel-Based Correlation Analysis: Generalized Correlation Function and Correntropy / 238
4.8 Kernel Matched Filter / 242
4.9 Discussion / 243
5 Correlative Learning in a Complex-Valued Domain 249
5.1 Preliminaries / 250
5.2 Complex-Valued Extensions of Correlation-Based Learning / 257
5.3 Kernel Methods for Complex-Valued Data / 277
5.4 Discussion / 280
6 ALOPEX: A CORRELATION-BASED LEARNING PARADIGM 283
6.1 Background / 283
6.2 The Basic ALOPEX Rule / 284
6.3 Variants of ALOPEX / 286
6.4 Discussion / 290
6.5 Monte Carlo Sampling-Based ALOPEX / 295
Appendix 6A: Asymptotic Analysis of ALOPEX Process / 303
Appendix 6B: Asymptotic Convergence Analysis of 2t-ALOPEX / 304
7 Case Studies 307
7.1 Hebbian Competition as Basis for Cortical Map Reorganization? / 308
7.2 Learning Neurocompensator: Model-Based Hearing Compensation Strategy / 320
7.3 Online Training of Artificial Neural Networks / 333
7.4 Kalman Filtering in Computational Neural Modeling / 340
8 Discussion 356
8.1 Summary: Why Correlation? / 356
8.2 Epilogue: What Next? / 359
Appendix A Autocorrelation and Cross-Correlation Functions 363
A.1 Autocorrelation Function / 363
A.2 Cross-Correlation Function / 364
A.3 Derivative Stochastic Processes / 367
Appendix B Stochastic Approximation
Appendix C Primer on Linear Algebra
C.1 Eigenanalysis / 372
C.2 Generalized Eigenvalue Problem / 375
C.3 SVD and Cholesky Factorization / 375
C.4 Gram-Schmidt Orthogonalization / 376
C.5 Principal Correlation / 377
Appendix D Probability Density and Entropy Estimators
D.1 Gram-Charlier Expansion / 379
D.2 Edgeworth Expansion / 381
D.3 Order Statistics / 381
D.4 Kernel Estimator / 382
Appendix E Expectation-Maximization Algorithm 384
E.1 Alternating Free-Energy Maximization / 384
E.2 Fitting Gaussian Mixture Model / 385
Index
