Sequential methods in pattern recognition and machine learning, Volume 52 (Mathematics in Science and Engineering)

✍ Scribed by Fu (editor)

• Publisher: Academic Press
• Year: 1969
• Tongue: English
• Leaves: 245
• Category: Library

✦ Synopsis

During the past decade there has been a considerable growth of interest in problems of pattern recognition and machine learning. This interest has created an increasing need for methods and techniques for the design of pattern recognition and learning systems. Many different approaches have been proposed. One of the most promising techniques for the solution of problems in pattern recognition and machine learning is the statistical theory of decision and estimation. This monograph treats the problems of pattern recognition and machine learning by use of sequential methods in statistical decision and estimation. In presenting the material, emphasis is placed upon the development of basic theory and computation algorithms in systematic fashion. The monograph is intended to be of use both as a reference for system engineers and computer scientists and as a supplementary textbook for courses in pattern recognition and adaptive and learning systems.

✦ Table of Contents

Front Cover
Sequential Methods in Pattern Recognition and Machine Learning
Copyright Page
Contents
Preface
Chapter 1. Introduction
1.1 Pattern Recognition
1.2 Deterministic Classification Techniques
1.3 Training in Linear Classifiers
1.4 Statistical Classification Techniques
1.5 Sequential Decision Model for Pattern Classification
1.6 Learning in Sequential Pattern Recognition Systems
1.7 Summary and Further Remarks
References
Chapter 2. Feature Selection and Feature Ordering
2.1 Feature Selection and Ordering—Information Theoretic Approach
2.2 Feature Selection and Ordering—Karhunen-Loève Expansion
2.3 Illustrative Examples
2.4 Summary and Further Remarks
References
Chapter 3. Forward Procedure for Finite Sequential Classification Using Modified Sequential Probability Ratio Test
3.1 Introduction
3.2 Modified Sequential Probability Ratio Test—Discrete Case
3.3 Modified Sequential Probability Ratio Test—Continuous Case
3.4 Procedure of Modified Generalized Sequential Probability Ratio Test
3.5 Experiments in Pattern Classification
3.6 Summary and Further Remarks
References
Chapter 4. Backward Procedure for Finite Sequential Recognition Using Dynamic Programming
4.1 Introduction
4.2 Mathematical Formulation and Basic Functional Equation
4.3 Reduction of Dimensionality
4.4 Experiments in Pattern Classification
4.5 Backward Procedure for Both Feature Ordering and Pattern Classification
4.6 Experiments in Feature Ordering and Pattern Classification
4.7 Use of Dynamic Programming for Feature-Subset Selection
4.8 Suboptimal Sequential Pattern Recognition
4.9 Summary and Further Remarks
References
Chapter 5. Nonparametric Procedure in Sequential Pattern Classification
5.1 Introduction
5.2 Sequential Ranks and Sequential Ranking Procedure
5.3 A Sequential Two-Sample Test Problem
5.4 Nonparametric Design of Sequential Pattern Classifiers
5.5 Analysis of Optimal Performance and a Multiclass Generalization
5.6 Experimental Results and Discussions
5.7 Summary and Further Remarks
References
Chapter 6. Bayesian Learning in Sequential Pattern Recognition Systems
6.1 Supervised Learning Using Bayesian Estimation Techniques
6.2 Nonsupervised Learning Using Bayesian Estimation Techniques
6.3 Bayesian Learning of Slowly Varying Patterns
6.4 Learning of Parameters Using an Empirical Bayes Approach
6.5 A General Model for Bayesian Learning Systems
6.6 Summary and Further Remarks
References
Chapter 7. Learning in Sequential Recognition Systems Using Stochastic Approximation
7.1 Supervised Learning Using Stochastic Approximation
7.2 Nonsupervised Learning Using Stochastic Approximation
7.3 A General Formulation of Nonsupervised Learning Systems Using Stochastic Approximation
7.4 Learning of Slowly Time-Varying Parameters Using Dynamic Stochastic Approximation
7.5 Summary and Further Remarks
References
Appendix A. Introduction to Sequential Analysis
1. Sequential Probability Ratio Test
2. Bayes' Sequential Decision Procedure
References
Appendix B. Optimal Properties of Generalized Karhunen–Loève Expansion
1. Derivation of Property (i)
2. Derivation of Property (ii)
Appendix C. Properties of the Modified SPRT
Appendix D. Enumeration of Some Combinations of the kjs and Derivation of Formula for the Reduction of Tables Required in the Computation of Risk Functions
Appendix E. Computations Required for the Feature Ordering and Pattern Classification Experiments Using Dynamic Programming
Appendix F. Stochastic Approximation: A Brief Survey
1. Robbins–Monro Procedure for Estimating the Zero of an Unknown Regression Function
2. Kiefer–Wolfowitz Procedure for Estimating the Extremum of an Unknown Regression Function
3. Dvoretzky's Generalized Procedure
4. Methods of Accelerating Convergence
5. Dynamic Stochastic Approximation
References
Appendix G. The Method of Potential Functions or Reproducing Kernels
1. The Estimation of a Function with Noise-Free Measurements
2. The Estimation of a Function with Noisy Measurements
3. Pattern Classification—Deterministic Case
4. Pattern Classification—Statistical Case
References
Author Index
Subject Index