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# Instruction to Statistical Pattern Recognition

## 1st Edition

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eBook ISBN: 9780323162784
Published Date: 28th January 1972
Page Count: 386
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## Description

Introduction to Statistical Pattern Recognition introduces the reader to statistical pattern recognition, with emphasis on statistical decision and estimation. Pattern recognition problems are discussed in terms of the eigenvalues and eigenvectors. Comprised of 11 chapters, this book opens with an overview of the formulation of pattern recognition problems. The next chapter is devoted to linear algebra, with particular reference to the properties of random variables and vectors. Hypothesis testing and parameter estimation are then discussed, along with error probability estimation and linear classifiers. The following chapters focus on successive approaches where the classifier is adaptively adjusted each time one sample is observed; feature selection and linear mapping for one distribution and multidistributions; and problems of nonlinear mapping. The final chapter describes a clustering algorithm and considers criteria for both parametric and nonparametric clustering. This monograph will serve as a text for the introductory courses of pattern recognition as well as a reference book for practitioners in the fields of mathematics and statistics.

Preface

Acknowledgments

Chapter 1 Introduction

1.1 Formulation of Pattern Recognition Problems

1.2 Chapter Outlines

Chapter 2 Random Vectors and Their Properties

2.1 Random Vectors and Their Distributions

2.2 Properties of Distributions

2.3 Transformation of Random Vectors

2.4 Various Properties of Eigenvalues and Eigenvectors

Standard Data

Computer Projects

Problems

Chapter 3 Hypothesis Testing

3.1 Simple Hypothesis Tests

3.2 Error Probability in Hypothesis Testing

3.3 Upper Bounds on Error Probability

3.4 Other Hypothesis Tests

3.5 Sequential Hypothesis Testing

Computer Projects

Problems

Chapter 4 Linear Classifiers

4.1 The Bayes Linear Classifier

4.2 Linear Discriminant Function for Minimum Error

4.3 Linear Discriminant Function for Minimum Mean-Square Error

4.4 Desired Output and Mean-Square Error

4.5 Other Discriminant Functions

Computer Projects

Problems

Chapter 5 Parameter Estimation

5.1 Estimation of Nonrandom Parameters

5.2 Estimation of Random Parameters

5.3 Interval Estimation

5.4 Estimation of the Probability of Error

Appendix 5-1 Calculation of the Bias between the C Method and the Leaving-One-Out Method

Computer Projects

Problems

Chapter 6 Estimation of Density Functions

6.1 Parzen Estimate

6.2 k-Nearest Neighbor Approach

6.3 Histogram Approach

6.4 Expansion by Basis Functions

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Problems

Chapter 7 Successive Parameter Estimation

7.1 Successive Adjustment of a Linear Classifier

7.2 Stochastic Approximation

7.3 Successive Bayes Estimation

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Problems

Chapter 8 Feature Selection and Linear Mapping for One Distribution

8.1 The Discrete Karhunen-Loève Expansion

8.2 Other Criteria for One Distribution

8.3 The Karhunen-Loève Expansion for Random Processes

8.4 Estimation of Eigenvalues and Eigenvectors

APPENDIX 8-1 Calculation of E{(ΦiTŜΦj)2}

APPENDIX 8-2 Rapid Eigenvalue-Eigenvector Calculation

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Problems

Chapter 9 Feature Selection and Linear Mapping for Multidistributions

9.1 General Properties of Class Separability

9.2 Discriminant Analysis

9.3 The Chernoff Bound and the Bhattacharyya Distance

9.4 Divergence

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Problems

Chapter 10 Nonlinear Mapping

10.1 Intrinsic Dimensionality of Data

10.2 Separability Enhancement by Nonlinear Mapping

10.3 Two-Dimensional Displays

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Chapter 11 Clustering

11.1 An Algorithm for Clustering

11.2 Parametric Clustering Criteria

11.3 Nonparametric Clustering Criteria

Computer Projects

References

Index

No. of pages:
386
Language:
English