Table of Contents

• CHAPTER 1: Organization of a Pattern Classifier
  • Design of a Classifie\x14 6
  • Choice of a Decision Rule 6
  • Linear Decision Rules\x14 7
  • Maximum Likelihood Classifier\x14 8
  • Determining Parametric Descriptions for Classifiers\x14 8
  • Supervised Learning 8
  • Unsupervised Learning 8
• CHAPTER 2 Review of Mathematical Principles 11
  • A Brief Review of Probability\x14 11
  • A review of linear algebra\x14 15
  • Introduction to Function Minimization\x14 20
  • Newton-Raphson\x14 22
  • Local vs. Global Minima\x14 25
  • Simulated Annealing\x14 26
  • How Simulated Annealing Works 27
  • Mean Field Annealing\x14 28
  • The prior probability 29
  • Using MFA to find the minimum 31
  • Annealing 32
  • MFA as a continuation method 32
• CHAPTER 3 The Maximum Likelihood Classifier
  • Parametric Pattern Classifiers\x14 39
  • Conditional Risk\x14 40
  • Conditional Risk: The 2-Class Case 41
  • Decision Regions\x14 43
  • The Minimax Rule 44
• CHAPTER 4 Estimating Normal Densities
  • Parameter Estimation, The Univariate Normal Case\x14 47
  • Estimating the Variance\x14 49
  • Estimating the Parameter for the Multivariate Normal Densities
• CHAPTER 5 Parametric Density Estimation Using Bayes Methods
• CHAPTER 6 Mixture Densities
  • Approximating a Mixture Density
  • Identifiability\x14 58
• CHAPTER 7 Linear Discriminant Functions
  • Introduction\x14 63
  • The Perceptron Criterion\x14 65
  • Convergence to a solution:\x14 67
  • Nonseparable Behavior\x14 69
  • Conclusion.\x14 69
• CHAPTER 8 Dimensionality reduction
  • The curse of dimensionality\x14 71
  • Fisher's Linear discriminant\x14 73
  • Feature selection by transform\x14 77
  • Dimensionality Reduction and the K-L Transform\x14 80
  • Derivation of the K-L Expansion 82
  • Properties of the K-L Expansion 85
  • Interpretation as a Hyperellipsoid 86
  • Use in Straight Line Filtering 86
  • Effectiveness of Features 87
  • Optimality 88
  • The K-L Expansion in Pattern Recognition 88
  • Selection of variables\x14 89
  • Branch and bound 89
• CHAPTER 9 Nonparametric methods for density estimation
  • The histogram\x14 91
  • Parzen windows\x14 95
  • k - Nearest-neighbor Methods\x14 99
• CHAPTER 10 Unsupervised Learning
  • Optimization methods in Clustering.\x14 115
  • Simulated Annealing 116
  • Branch and Bound 116
  • Vector quantization.\x14 117
  • Winner-take-all approaches\x14 117
  • Kohonen feature maps 118
• CHAPTER 11 Neural Networks for pattern classification
  • Types of Neural Networks:\x14 126
  • The backpropagation algorithm:\x14 126
• CHAPTER 12 References 133
  • Literature Cited(That I havent needed yet)\x14 140