Instruction to Statistical Pattern Recognition

Instruction to Statistical Pattern Recognition

1st Edition - January 1, 1972

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  • Editor: Keinosuke Fukunaga
  • eBook ISBN: 9780323162784

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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.

Table of Contents

  • Preface


    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


    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


    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


    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


    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

    Computer Projects


    Chapter 7 Successive Parameter Estimation

    7.1 Successive Adjustment of a Linear Classifier

    7.2 Stochastic Approximation

    7.3 Successive Bayes Estimation

    Computer Projects


    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

    Computer Projects


    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

    Computer Projects


    Chapter 10 Nonlinear Mapping

    10.1 Intrinsic Dimensionality of Data

    10.2 Separability Enhancement by Nonlinear Mapping

    10.3 Two-Dimensional Displays

    Computer Projects

    Chapter 11 Clustering

    11.1 An Algorithm for Clustering

    11.2 Parametric Clustering Criteria

    11.3 Nonparametric Clustering Criteria

    11.4 Additional Clustering Procedures

    Computer Projects



Product details

  • No. of pages: 386
  • Language: English
  • Copyright: © Academic Press 1972
  • Published: January 1, 1972
  • Imprint: Academic Press
  • eBook ISBN: 9780323162784

About the Editor

Keinosuke Fukunaga

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