Statistical and Neural Classifiers: An Integrated Approach to Design - Brossura
Libro 26 di 86: Advances in Computer Vision and Pattern Recognition
Sinossi
1. Quick Overview.- 1.1 The Classifier Design Problem.- 1.2 Single Layer and Multilayer Perceptrons.- 1.3 The SLP as the Euclidean Distance and the Fisher Linear Classifiers.- 1.4 The Generalisation Error of the EDC and the Fisher DF.- 1.5 Optimal Complexity - The Scissors Effect.- 1.6 Overtraining in Neural Networks.- 1.7 Bibliographical and Historical Remarks.- 2. Taxonomy of Pattern Classification Algorithms.- 2.1 Principles of Statistical Decision Theory.- 2.2 Four Parametric Statistical Classifiers.- 2.2.1 The Quadratic Discriminant Function.- 2.2.2 The Standard Fisher Linear Discriminant Function.- 2.2.3 The Euclidean Distance Classifier.- 2.2.4 The Anderson-Bahadur Linear DF.- 2.3 Structures of the Covariance Matrices.- 2.3.1 A Set of Standard Assumptions.- 2.3.2 Block Diagonal Matrices.- 2.3.3 The Tree Type Dependence Models.- 2.3.4 Temporal Dependence Models.- 2.4 The Bayes Predictive Approach to Design Optimal Classification Rules.- 2.4.1 A General Theory.- 2.4.2 Learning the Mean Vector.- 2.4.3 Learning the Mean Vector and CM.- 2.4.4 Qualities and Shortcomings.- 2.5. Modifications of the Standard Linear and Quadratic DF.- 2.5.1 A Pseudo-Inversion of the Covariance Matrix.- 2.5.2 Regularised Discriminant Analysis (RDA).- 2.5.3 Scaled Rotation Regularisation.- 2.5.4 Non-Gausian Densities.- 2.5.5 Robust Discriminant Analysis.- 2.6 Nonparametric Local Statistical Classifiers.- 2.6.1 Methods Based on Mixtures of Densities.- 2.6.2 Piecewise-Linear Classifiers.- 2.6.3 The Parzen Window Classifier.- 2.6.4 The k-NN Rule and a Calculation Speed.- 2.6.5 Polynomial and Potential Function Classifiers.- 2.7 Minimum Empirical Error and Maximal Margin Linear Classifiers.- 2.7.1 The Minimum Empirical Error Classifier.- 2.7.2 The Maximal Margin Classifier.- 2.7.3 The Support Vector Machine.- 2.8 Piecewise-Linear Classifiers.- 2.8.1 Multimodal Density Based Classifiers.- 2.8.2 Architectural Approach to Design of the Classifiers.- 2.8.3 Decision Tree Classifiers.- 2.9 Classifiers for Categorical Data.- 2.9.1 Multinornial Classifiers.- 2.9.2 Estimation of Parameters.- 2.9.3 Decision Tree and the Multinornial Classifiers.- 2.9.4 Linear Classifiers.- 2.9.5 Nonparametric Local Classifiers.- 2.10 Bibliographical and Historical Remarks.- 3. Performance and the Generalisation Error.- 3.1 Bayes, Conditional, Expected, and Asymptotic Probabilities of Misclassification.- 3.1.1 The Bayes Probability of Misclassification.- 3.1.2 The Conditional Probability of Misclassification.- 3.1.3 The Expected Probability of Misclassification.- 3.1.4 The Asymptotic Probability of Misclassification.- 3.1.5 Learning Curves: An Overview of Different Analysis Methods.- 3.1.6 Error Estimation.- 3.2 Generalisation Error of the Euclidean Distance Classifier.- 3.2.1 The Classification Algorithm.- 3.2.2 Double Asymptotics in the Error Analysis.- 3.2.3 The Spherical Gaussian Case.- 3.2.3.1 The Case N2 = N1.- 3.2.3.2 The Case N2 ? N1.- 3.3 Most Favourable and Least Favourable Distributions of the Data.- 3.3.1 The Non-Spherical Gaussian Case.- 3.3.2 The Most Favourable Distributions of the Data.- 3.3.3 The Least Favourable Distributions of the Data.- 3.3.4 Intrinsic Dimensionality.- 3.4 Generalisation Errors for Modifications of the Standard Linear Classifier.- 3.4.1 The Standard Fisher Linear DF.- 3.4.2 The Double Asymptotics for the Expected Error.- 3.4.3 The Conditional Probability of Misc1assification.- 3.4.4 A Standard Deviation of the Conditional Error.- 3.4.5 Favourable and Unfavourable Distributions.- 3.4.6 Theory and Real-World Problems.- 3.4.7 The Linear Classifier D for the Diagonal CM.- 3.4.8 The Pseudo-Fisher Classifier.- 3.4.9 The Regularised Discriminant Analysis.- 3.5 Common Parameters in Different Competing Pattern Classes.- 3.5.1 The Generalisation Error of the Quadratic DF.- 3.5.2 The Effect of Common Parameters in Two Competing Classes.- 3.5.3 Unequal Sampie Sizes in Plug-In Classifiers.- 3.6 Minimum Empirical Error and Maximal Margin Classifiers.- 3.6
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