Correlative Learning A Basis for Brain and

Correlative Learning: A Basis for Brain and Adaptive Systems provides a bridge between three disciplines: computational neuroscience, neural networks, and signal processing. First, the authors lay down the preliminary neuroscience background for engineers. The book also presents an overview of the role of correlation in the human brain as well as in the adaptive signal processing world; unifies many well-established synaptic adaptations (learning) rules within the correlation-based learning framework, focusing on a particular correlative learning paradigm, ALOPEX; and presents case studies that illustrate how to use different computational tools and ALOPEX to help readers understand certain brain functions or fit specific engineering applications.

Zhe Chen, PhD, is currently a Research Fellow in the Neuroscience Statistics Research Laboratory at Harvard Medical School.

Simon Haykin, PhD, DSc, is a Distinguished University Professor in the Department of Electrical and Computer Engineering at McMaster University, Ontario, Canada.

Jos J. Eggermont, PhD, is a Professor in the Departments of Physiology & Biophysics and Psychology at the University of Calgary, Alberta, Canada.

Suzanna Becker, PhD, is a Professor in the Department of Psychology, Neuroscience, and Behavior at McMaster University, Ontario, Canada.

Foreword
Preface
Acknowledgments
Acronyms
Introduction
The Correlative Brain
Background
Spiking Neurons
Neocortex
Receptive fields
Thalamus
Hippocampus
Correlation Detection in Single Neurons
Correlation in Ensembles of Neurons: Synchrony and Population Coding
Correlation is the Basis of Novelty Detection and Learning
Correlation in Sensory Systems: Coding, Perception, and Development
Correlation in Memory Systems
Correlation in Sensory-Motor Learning
Correlation, Feature Binding, and Attention
Correlation and Cortical Map Changes after Peripheral Lesions and Brain Stimulation
Discussion
Correlation in Signal Processing
Correlation and Spectrum Analysis
Stationary Process
Non-stationary Process
Locally Stationary Process
Cyclostationary Process
Hilbert Spectrum Analysis
Higher Order Correlation-based Bispectra Analysis
Higher Order Functions of Time, Frequency, Lag, and Doppler
Spectrum Analysis of Random Point Process
Wiener Filter
Least-Mean-Square Filter
Recursive Least-Squares Filter
Matched Filter
Higher Order Correlation-Based Filtering
Correlation Detector
Coherent Detection
Correlation Filter for Spatial Target Detection
Correlation Method for Time-Delay Estimation
Correlation-Based Statistical Analysis
Principal Component Analysis
Factor Analysis
Canonical Correlation Analysis
Fisher Linear Discriminant Analysis
Common Spatial Pattern Analysis
Discussion
Appendix: Eigenanalysis of Autocorrelation Function of Nonstationary Process
Appendix: Estimation of the Intensity and Correlation Functions of Stationary Random Point Process
Appendix: Derivation of Learning Rules with Quasi-Newton Method
Correlation-Based Neural Learning and Machine Learning
Correlation as a Mathematical Basis for Learning
Hebbian and Anti-Hebbian Rules (Revisited)
Covariance Rule
Grossberg's Gated Steepest Descent
Competitive Learning Rule
BCM Learning Rule
Local PCA Learning Rule
Generalizations of PCA Learning
CCA Learning Rule
Wake-Sleep Learning Rule for Factor Analysis
Boltzmann Learning Rule
Perceptron Rule and Error-Correcting Learning Rule
Differential Hebbian Rule and Temporal Hebbian Learning
Temporal Difference and Reinforcement Learning
General Correlative Learning and Potential Function
Information-Theoretic Learning
Mutual Information vs. Correlation
Barlow's Postulate
Hebbian Learning and Maximum Entropy
Imax Algorithm
Local Decorrelative Learning
Blind Source Separation
Independent Component Analysis
Slow Feature Analysis
Energy-Efficient Hebbian Learning
Discussion
Correlation-Based Computational Neural Models
Correlation Matrix Memory
Hopfield Network
Brain-State-in-a-Box Model
Autoencoder Network
Novelty Filter
Neuronal Synchrony and Binding
Oscillatory Correlation
Modeling Auditory Functions
Correlations in the Olfactory System
Correlations in the Visual System
Elastic Net
CMAC and Motor Learning
Summarizing Remarks
Appendix: Mathematical Analysis of Hebbian Learning
Appendix: Necessity and Convergence of Anti-Hebbian Learning
Appendix: Link Between the Hebbian Rule and Gradient Descent
Appendix: Reconstruction Error in L
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Correlative Learning A Basis for Brain and Adaptive Systems

Summary

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Table of Contents

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