Pattern Recognition

, by Theodoridis, Sergios; Koutroumbas, Konstantinos

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ISBN: 9780126858754 | 0126858756
Cover: Hardcover
Copyright: 3/1/2003

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*Approaches pattern recognition from the designer's point of view*New edition highlights latest developments in this growing field, including independent components and support vector machines, not available elsewhere*Supplemented by computer examples selected from applications of interestPattern recognition is a scientific discipline that is becoming increasingly important in the age of automation and information handling and retrieval. This volume's unifying treatment covers the entire spectrum of pattern recognition applications, from image analysis to speech recognition and communications. This book presents cutting-edge material on neural networks, - a set of linked microprocessors that can form associations and uses pattern recognition to "learn". A direct result of more than 10 years of teaching experience, the text was developed by the authors through use in their own classrooms.

Preface

xiii

Introduction

(12)

Is Pattern Recognition Important?

(2)

Features, Feature Vectors, and Classifiers

(3)

Supervised Versus Unsupervised Pattern Recognition

(2)

Outline of the Book

(5)

Classifiers Based On Bayes Decision Theory

(42)

Introduction

(1)

Bayes Decision Theory

(6)

Discriminant Functions and Decision Surfaces

(1)

Bayesian Classification for Normal Distributions

(7)

Estimation of Unknown Probability Density Functions

(17)

Maximum Likelihood Parameter Estimation

(3)

Maximum a Posteriori Probability Estimation

(1)

Bayesian Inference

(2)

Maximum Entropy Estimation

(1)

Mixture Models

(4)

Nonparametric Estimation

(5)

The Nearest Neighbor Rule

(11)

Linear Classifiers

(38)

Introduction

(1)

Linear Discriminant Functions and Decision Hyperplanes

(2)

The Perceptron Algorithm

(8)

Least Squares Methods

(7)

Mean Square Error Estimation

(3)

Stochastic Approximation and the LMS Algorithm

(2)

Sum of Error Squares Estimation

(2)

Mean Square Estimation Revisited

(5)

Mean Square Error Regression

(1)

MSE Estimates Posterior Class Probabilities

(3)

The Bias-Variance Dilemma

(1)

Support Vector Machines

(16)

Separable Classes

(5)

Nonseparable Classes

(11)

Nonlinear Classifiers

(70)

Introduction

(1)

The XOR Problem

(1)

The Two-Layer Perceptron

(7)

Classification Capabilities of the Two-Layer Perceptron

(3)

Three-Layer Perceptrons

101

(1)

Algorithms Based on Exact Classification of the Training Set

102

(2)

The Backpropagation Algorithm

104

(8)

Variations on the Backpropagation Theme

112

(3)

The Cost Function Choice

115

(3)

Choice of the Network Size

118

(6)

A Simulation Example

124

(2)

Networks With Weight Sharing

126

(1)

Generalized Linear Classifiers

127

(2)

Capacity of the l-Dimensional Space in Linear Dichotomies

129

(2)

Polynomial Classifiers

131

(2)

Radial Basis Function Networks

133

(4)

Universal Approximators

137

(2)

Support Vector Machines: The Nonlinear Case

139

(4)

Decision Trees

143

(7)

Set of Questions

146

(1)

Splitting Criterion

146

(1)

Stop-Splitting Rule

147

(1)

Class Assignment Rule

147

(3)

Discussion

150

(13)

Feature Selection

163

(44)

Introduction

163

(1)

Preprocessing

164

(1)

Outlier Removal

164

(1)

Data Normalization

165

(1)

Missing Data

165

(1)

Feature Selection Based on Statistical Hypothesis Testing

165

(8)

Hypothesis Testing Basics

166

(5)

Application of the t-Test in Feature Selection

171

(2)

The Receiver Operating Characteristics CROC Curve

173

(1)

Class Separability Measures

174

(7)

Divergence

174

(3)

Chernoff Bound and Bhattacharyya Distance

177

(2)

Scatter Matrices

179

(2)

Feature Subset Selection

181

(6)

Scalar Feature Selection

182

(1)

Feature Vector Selection

183

(4)

Optimal Feature Generation

187

(4)

Neural Networks and Feature Generation/Selection

191

(2)

A Hint on the Vapnik--Chernovenkis Learning Theory

193

(14)

Feature Generation I: Linear Transforms

207

(62)

Introduction

207

(1)

Basis Vectors and Images

208

(2)

The Karhunen--Loeve Transform

210

(5)

The Singular Value Decomposition

215

(4)

Independent Component Analysis

219

(7)

ICA Based on Second- and Fourth-Order Cumulants

221

(1)

ICA Based on Mutual Information

222

(4)

An ICA Simulation Example

226

(1)

The Discrete Fourier Transform (DFT)

226

(4)

One-Dimensional DFT

227

(2)

Two-Dimensional DFT

229

(1)

The Discrete Cosine and Sine Transforms

230

(1)

The Hadamard Transform

231

(2)

The Haar Transform

233

(2)

The Haar Expansion Revisited

235

(4)

Discrete Time Wavelet Transform (DTWT)

239

(10)

The Multiresolution Interpretation

249

(3)

Wavelet Packets

252

(1)

A Look at Two-Dimensional Generalizations

252

(3)

Applications

255

(14)

Feature Generation II

269

(52)

Introduction

269

(1)

Regional Features

270

(24)

Features for Texture Characterization

270

(9)

Local Linear Transforms for Texture Feature Extraction

279

(2)

Moments

281

(5)

Parametric Models

286

(8)

Features for Shape and Size Characterization

294

(9)

Fourier Features

295

(3)

Chain Codes

298

(3)

Moment-Based Features

301

(1)

Geometric Features

302

(1)

A Glimpse at Fractals

303

(18)

Self-Similarity and Fractal Dimension

303

(3)

Fractional Brownian Motion

306

(15)

Template Matching

321

(30)

Introduction

321

(1)

Measures Based on Optimal Path Searching Techniques

322

(15)

Bellman's Optimality Principle and Dynamic Programming

324

(1)

The Edit Distance

325

(4)

Dynamic Time Warping in Speech Recognition

329

(8)

Measures Based on Correlations

337

(6)

Deformable Template Models

343

(8)

Context-Dependent Classification

351

(34)

Introduction

351

(1)

The Bayes Classifier

351

(1)

Markov Chain Models

352

(1)

The Viterbi Algorithm

353

(3)

Channel Equalization

356

(5)

Hidden Markov Models

361

(12)

Training Markov Models via Neural Networks

373

(2)

A discussion of Markov Random Fields

375

(10)

System Evaluation

385

(12)

Introduction

385

(1)

Error Counting Approach

385

(2)

Exploiting the Finite Size of the Data Set

387

(3)

A Case Study From Medical Imaging

390

(7)

Clustering: Basic Concepts

397

(32)

Introduction

397

(7)

Applications of Cluster Analysis

400

(1)

Types of Features

401

(1)

Definitions of Clustering

402

(2)

Proximity Measures

404

(25)

Definitions

404

(3)

Proximity Measures between Two Points

407

(11)

Proximity Functions between a Point and a Set

418

(5)

Proximity Functions between Two Sets

423

(6)

Clustering Algorithms I: Sequential Algorithms

429

(20)

Introduction

429

(2)

Number of Possible Clusterings

429

(2)

Categories of Clustering Algorithms

431

(2)

Sequential Clustering Algorithms

433

(4)

Estimation of the Number of Clusters

435

(2)

A Modification of BSAS

437

(1)

A Two-Threshold Sequential Scheme

438

(3)

Refinement Stages

441

(2)

Neural Network Implementation

443

(6)

Description of the Architecture

443

(1)

Implementation of the BSAS Algorithm

444

(5)

Clustering Algorithms II: Hierarchical Algorithms

449

(40)

Introduction

449

(1)

Agglomerative Algorithms

450

(26)

Definition of Some Useful Quantities

451

(2)

Agglomerative Algorithms Based on Matrix Theory

453

(8)

Monotonicity and Crossover

461

(3)

Implementational Issues

464

(1)

Agglomerative Algorithms Based on Graph Theory

464

(10)

Ties in the Proximity Matrix

474

(2)

The Cophenetic Matrix

476

(2)

Divisive Algorithms

478

(2)

Choice of the Best Number of Clusters

480

(9)

Clustering Algorithms III: Schemes Based on Function Optimization

489

(56)

Introduction

489

(2)

Mixture Decomposition Schemes

491

(9)

Compact and Hyperellipsoidal Clusters

493

(4)

A Geometrical Interpretation

497

(3)

Fuzzy Clustering Algorithms

500

(22)

Point Representatives

505

(2)

Quadric Surfaces as Representatives

507

(10)

Hyperplane Representatives

517

(2)

Combining Quadric and Hyperplane Representatives

519

(2)

A Geometrical Interpretation

521

(1)

Convergence Aspects of the Fuzzy Clustering Algorithms

522

(1)

Alternating Cluster Estimation

522

(1)

Possibilistic Clustering

522

(7)

The Mode-Seeking Property

526

(3)

An Alternative Possibilistic Scheme

529

(1)

Hard Clustering Algorithms

529

(4)

The Isodata or k-Means or c-Means Algorithm

531

(2)

Vector Quantization

533

(12)

Clustering Algorithms IV

545

(46)

Introduction

545

(1)

Clustering Algorithms Based on Graph Theory

545

(7)

Minimum Spanning Tree Algorithms

546

(3)

Algorithms Based on Regions of Influence

549

(1)

Algorithms Based on Directed Trees

550

(2)

Competitive Learning Algorithms

552

(9)

Basic Competitive Learning Algorithm

554

(2)

Leaky Learning Algorithm

556

(1)

Conscientious Competitive Learning Algorithms

556

(2)

Competitive Learning--Like Algorithms Associated with Cost Functions

558

(1)

Self-Organizing Maps

559

(1)

Supervised Learning Vector Quantization

560

(1)

Branch and Bound Clustering Algorithms

561

(3)

Binary Morphology Clustering Algorithms (BMCAs)

564

(9)

Discretization

564

(1)

Morphological Operations

565

(3)

Determination of the Clusters in a Discrete Binary Set

568

(2)

Assignment of Feature Vectors to Clusters

570

(1)

The Algorithmic Scheme

571

(2)

Boundary Detection Algorithms

573

(3)

Valley-Seeking Clustering Algorithms

576

(2)

Clustering Via Cost Optimization (Revisited)

578

(4)

Simulated Annealing

579

(1)

Deterministic Annealing

580

(2)

Clustering Using Genetic Algorithms

582

(1)

Other Clustering Algorithms

583

(8)

Cluster Validity

591

(52)

Introduction

591

(1)

Hypothesis Testing Revisited

592

(2)

Hypothesis Testing in Cluster Validity

594

(11)

External Criteria

596

(6)

Internal Criteria

602

(3)

Relative Criteria

605

(16)

Hard Clustering

608

(6)

Fuzzy Clustering

614

(7)

Validity of Individual Clusters

621

(3)

External Criteria

621

(1)

Internal Criteria

622

(2)

Clustering Tendency

624

(19)

Tests for Spatial Randomness

628

(15)

Appendix A Hints from Probability and Statistics

643

(12)

Appendix B Linear Algebra Basics

655

(4)

Appendix C Cost Function Optimization

659

(18)

Appendix D Basic Definitions from Linear Systems Theory

677

(4)

Index

681

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Pattern Recognition

Summary

Table of Contents

Supplemental Materials