Preface |
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xix | |
Notation |
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xxiii | |
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1 Introduction to Statistical Pattern Recognition |
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1 | (32) |
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1.1 Statistical Pattern Recognition |
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1 | (3) |
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1 | (1) |
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2 | (2) |
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1.2 Stages in a Pattern Recognition Problem |
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4 | (2) |
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6 | (1) |
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1.4 Approaches to Statistical Pattern Recognition |
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7 | (1) |
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1.5 Elementary Decision Theory |
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8 | (12) |
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1.5.1 Bayes' Decision Rule for Minimum Error |
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8 | (4) |
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1.5.2 Bayes' Decision Rule for Minimum Error - Reject Option |
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12 | (1) |
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1.5.3 Bayes' Decision Rule for Minimum Risk |
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13 | (2) |
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1.5.4 Bayes' Decision Rule for Minimum Risk - Reject Option |
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15 | (1) |
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1.5.5 Neyman-Pearson Decision Rule |
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15 | (3) |
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18 | (1) |
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19 | (1) |
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1.6 Discriminant Functions |
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20 | (7) |
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20 | (1) |
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1.6.2 Linear Discriminant Functions |
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21 | (2) |
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1.6.3 Piecewise Linear Discriminant Functions |
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23 | (1) |
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1.6.4 Generalised Linear Discriminant Function |
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24 | (2) |
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26 | (1) |
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27 | (2) |
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29 | (1) |
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29 | (2) |
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31 | (2) |
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2 Density Estimation - Parametric |
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33 | (37) |
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33 | (1) |
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2.2 Estimating the Parameters of the Distributions |
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34 | (1) |
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2.2.1 Estimative Approach |
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34 | (1) |
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2.2.2 Predictive Approach |
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35 | (1) |
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2.3 The Gaussian Classifier |
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35 | (5) |
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35 | (2) |
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2.3.2 Derivation of the Gaussian Classifier Plug-In Estimates |
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37 | (2) |
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2.3.3 Example Application Study |
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39 | (1) |
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2.4 Dealing with Singularities in the Gaussian Classifier |
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40 | (6) |
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40 | (1) |
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40 | (1) |
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2.4.3 Projection onto a Subspace |
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41 | (1) |
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2.4.4 Linear Discriminant Function |
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41 | (1) |
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2.4.5 Regularised Discriminant Analysis |
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42 | (2) |
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2.4.6 Example Application Study |
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44 | (1) |
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2.4.7 Further Developments |
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45 | (1) |
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46 | (1) |
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2.5 Finite Mixture Models |
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46 | (17) |
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46 | (2) |
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2.5.2 Mixture Models for Discrimination |
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48 | (1) |
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2.5.3 Parameter Estimation for Normal Mixture Models |
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49 | (2) |
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2.5.4 Normal Mixture Model Covariance Matrix Constraints |
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51 | (1) |
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2.5.5 How Many Components? |
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52 | (3) |
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2.5.6 Maximum Likelihood Estimation via EM |
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55 | (5) |
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2.5.7 Example Application Study |
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60 | (2) |
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2.5.8 Further Developments |
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62 | (1) |
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63 | (1) |
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63 | (3) |
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2.7 Summary and Discussion |
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66 | (1) |
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66 | (1) |
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67 | (1) |
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67 | (3) |
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3 Density Estimation - Bayesian |
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70 | (80) |
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70 | (3) |
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72 | (1) |
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3.1.2 Recursive Calculation |
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72 | (1) |
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73 | (1) |
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73 | (14) |
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73 | (2) |
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3.2.2 Estimating the Mean of a Normal Distribution with Known Variance |
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75 | (4) |
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3.2.3 Estimating the Mean and the Covariance Matrix of a Multivariate Normal Distribution |
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79 | (6) |
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3.2.4 Unknown Prior Class Probabilities |
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85 | (2) |
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87 | (1) |
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3.3 Bayesian Sampling Schemes |
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87 | (8) |
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87 | (1) |
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87 | (2) |
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3.3.3 Sampling Version of the Bayesian Classifier |
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89 | (1) |
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89 | (1) |
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90 | (2) |
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3.3.6 Importance Sampling |
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92 | (3) |
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3.4 Markov Chain Monte Carlo Methods |
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95 | (21) |
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95 | (1) |
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95 | (8) |
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3.4.3 Metropolis-Hastings Algorithm |
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103 | (4) |
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107 | (1) |
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3.4.5 Reversible Jump Markov Chain Monte Carlo |
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108 | (1) |
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109 | (2) |
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3.4.7 MCMC Example - Estimation of Noisy Sinusoids |
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111 | (4) |
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115 | (1) |
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3.4.9 Notes and References |
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116 | (1) |
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3.5 Bayesian Approaches to Discrimination |
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116 | (3) |
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3.5.1 Labelled Training Data |
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116 | (1) |
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3.5.2 Unlabelled Training Data |
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117 | (2) |
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3.6 Sequential Monte Carlo Samplers |
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119 | (7) |
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119 | (2) |
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121 | (4) |
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125 | (1) |
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126 | (11) |
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126 | (1) |
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126 | (3) |
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3.7.3 Factorised Variational Approximation |
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129 | (2) |
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131 | (4) |
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3.7.5 Use of the Procedure for Model Selection |
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135 | (1) |
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3.7.6 Further Developments and Applications |
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136 | (1) |
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137 | (1) |
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3.8 Approximate Bayesian Computation |
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137 | (7) |
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137 | (1) |
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3.8.2 ABC Rejection Sampling |
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138 | (2) |
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140 | (1) |
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3.8.4 ABC Population Monte Carlo Sampling |
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141 | (1) |
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142 | (1) |
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143 | (1) |
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3.9 Example Application Study |
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144 | (1) |
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145 | (1) |
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3.11 Summary and Discussion |
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146 | (1) |
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147 | (1) |
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3.13 Notes and References |
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147 | (1) |
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148 | (2) |
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4 Density Estimation - Nonparametric |
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150 | (71) |
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150 | (2) |
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4.1.1 Basic Properties of Density Estimators |
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150 | (2) |
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4.2 k-Nearest-Neighbour Method |
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152 | (28) |
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4.2.1 k-Nearest-Neighbour Classifier |
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152 | (2) |
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154 | (3) |
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4.2.3 Choice of Distance Metric |
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157 | (2) |
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4.2.4 Properties of the Nearest-Neighbour Rule |
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159 | (1) |
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4.2.5 Linear Approximating and Eliminating Search Algorithm |
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159 | (4) |
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4.2.6 Branch and Bound Search Algorithms: kd-Trees |
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163 | (7) |
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4.2.7 Branch and Bound Search Algorithms: Ball-Trees |
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170 | (4) |
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174 | (3) |
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4.2.9 Example Application Study |
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177 | (1) |
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4.2.10 Further Developments |
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178 | (1) |
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179 | (1) |
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180 | (14) |
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4.3.1 Data Adaptive Histograms |
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181 | (1) |
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4.3.2 Independence Assumption (Naive Bayes) |
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181 | (1) |
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182 | (1) |
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4.3.4 Maximum Weight Dependence Trees |
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183 | (3) |
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186 | (4) |
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4.3.6 Example Application Study - Naive Bayes Text Classification |
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190 | (3) |
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193 | (1) |
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194 | (10) |
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197 | (1) |
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4.4.2 Multivariate Extension |
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198 | (1) |
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4.4.3 Choice of Smoothing Parameter |
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199 | (2) |
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201 | (1) |
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4.4.5 Example Application Study |
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202 | (1) |
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4.4.6 Further Developments |
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203 | (1) |
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203 | (1) |
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4.5 Expansion by Basis Functions |
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204 | (3) |
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207 | (6) |
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207 | (1) |
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207 | (1) |
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208 | (1) |
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4.6.4 Estimating Copula Probability Density Functions |
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209 | (2) |
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211 | (1) |
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212 | (1) |
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213 | (3) |
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4.7.1 Comparative Studies |
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216 | (1) |
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4.8 Summary and Discussion |
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216 | (1) |
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217 | (1) |
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4.10 Notes and References |
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217 | (1) |
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218 | (3) |
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5 Linear Discriminant Analysis |
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221 | (53) |
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221 | (1) |
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222 | (14) |
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222 | (5) |
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227 | (1) |
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5.2.4 Least Mean-Squared-Error Procedures |
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228 | (7) |
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5.2.5 Further Developments |
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235 | (1) |
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235 | (1) |
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5.3 Multiclass Algorithms |
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236 | (13) |
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236 | (1) |
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5.3.2 Error-Correction Procedure |
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237 | (1) |
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5.3.3 Fisher's Criterion - Linear Discriminant Analysis |
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238 | (3) |
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5.3.4 Least Mean-Squared-Error Procedures |
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241 | (5) |
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246 | (1) |
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5.3.6 Example Application Study |
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246 | (1) |
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5.3.7 Further Developments |
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247 | (1) |
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248 | (1) |
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5.4 Support Vector Machines |
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249 | (14) |
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249 | (1) |
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5.4.2 Linearly Separable Two-Class Data |
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249 | (4) |
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5.4.3 Linearly Nonseparable Two-Class Data |
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253 | (3) |
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256 | (1) |
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5.4.5 SVMs for Regression |
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257 | (2) |
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259 | (3) |
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5.4.7 Example Application Study |
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262 | (1) |
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263 | (1) |
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5.5 Logistic Discrimination |
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263 | (5) |
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263 | (1) |
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5.5.2 Maximum Likelihood Estimation |
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264 | (2) |
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5.5.3 Multiclass Logistic Discrimination |
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266 | (1) |
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5.5.4 Example Application Study |
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267 | (1) |
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5.5.5 Further Developments |
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267 | (1) |
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268 | (1) |
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268 | (1) |
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5.7 Summary and Discussion |
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268 | (1) |
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269 | (1) |
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270 | (1) |
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270 | (4) |
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6 Nonlinear Discriminant Analysis - Kernel and Projection Methods |
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274 | (48) |
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274 | (2) |
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6.2 Radial Basis Functions |
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276 | (15) |
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276 | (2) |
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6.2.2 Specifying the Model |
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278 | (1) |
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6.2.3 Specifying the Functional Form |
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278 | (1) |
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6.2.4 The Positions of the Centres |
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279 | (2) |
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6.2.5 Smoothing Parameters |
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281 | (1) |
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6.2.6 Calculation of the Weights |
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282 | (2) |
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6.2.7 Model Order Selection |
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284 | (1) |
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285 | (1) |
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286 | (2) |
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288 | (1) |
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6.2.11 Example Application Study |
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288 | (1) |
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6.2.12 Further Developments |
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289 | (1) |
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290 | (1) |
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6.3 Nonlinear Support Vector Machines |
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291 | (7) |
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291 | (1) |
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6.3.2 Binary Classification |
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291 | (1) |
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292 | (1) |
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293 | (1) |
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294 | (1) |
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6.3.6 Probability Estimates |
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294 | (2) |
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6.3.7 Nonlinear Regression |
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296 | (1) |
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6.3.8 Example Application Study |
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296 | (1) |
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6.3.9 Further Developments |
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297 | (1) |
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298 | (1) |
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6.4 The Multilayer Perceptron |
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298 | (16) |
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298 | (1) |
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6.4.2 Specifying the MLP Structure |
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299 | (1) |
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6.4.3 Determining the MLP Weights |
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300 | (7) |
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6.4.4 Modelling Capacity of the MLP |
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307 | (1) |
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6.4.5 Logistic Classification |
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307 | (3) |
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6.4.6 Example Application Study |
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310 | (1) |
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6.4.7 Bayesian MLP Networks |
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311 | (2) |
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313 | (1) |
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313 | (1) |
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314 | (2) |
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6.6 Summary and Discussion |
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316 | (1) |
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317 | (1) |
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318 | (1) |
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318 | (4) |
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7 Rule and Decision Tree Induction |
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322 | (39) |
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322 | (1) |
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323 | (19) |
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323 | (3) |
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7.2.2 Decision Tree Construction |
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326 | (1) |
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7.2.3 Selection of the Splitting Rule |
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327 | (3) |
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7.2.4 Terminating the Splitting Procedure |
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330 | (2) |
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7.2.5 Assigning Class Labels to Terminal Nodes |
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332 | (1) |
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7.2.6 Decision Tree Pruning - Worked Example |
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332 | (5) |
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7.2.7 Decision Tree Construction Methods |
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337 | (2) |
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339 | (1) |
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7.2.9 Example Application Study |
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340 | (1) |
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7.2.10 Further Developments |
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341 | (1) |
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342 | (1) |
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342 | (9) |
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342 | (3) |
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7.3.2 Generating Rules from a Decision Tree |
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345 | (1) |
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7.3.3 Rule Induction Using a Sequential Covering Algorithm |
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345 | (5) |
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7.3.4 Example Application Study |
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350 | (1) |
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7.3.5 Further Developments |
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351 | (1) |
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351 | (1) |
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7.4 Multivariate Adaptive Regression Splines |
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351 | (5) |
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351 | (1) |
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7.4.2 Recursive Partitioning Model |
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351 | (4) |
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7.4.3 Example Application Study |
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355 | (1) |
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7.4.4 Further Developments |
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355 | (1) |
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356 | (1) |
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356 | (2) |
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7.6 Summary and Discussion |
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358 | (1) |
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358 | (1) |
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359 | (1) |
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359 | (2) |
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361 | (43) |
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361 | (1) |
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8.2 Characterising a Classifier Combination Scheme |
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362 | (8) |
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363 | (3) |
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366 | (2) |
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368 | (1) |
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8.2.4 Form of Component Classifiers |
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368 | (1) |
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369 | (1) |
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369 | (1) |
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370 | (6) |
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370 | (1) |
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8.3.2 Bayesian Approaches |
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371 | (2) |
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8.3.3 Neyman-Pearson Formulation |
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373 | (1) |
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374 | (1) |
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375 | (1) |
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8.4 Classifier Combination Methods |
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376 | (23) |
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376 | (1) |
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377 | (1) |
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8.4.3 Min, Max and Median Combiners |
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378 | (1) |
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379 | (1) |
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379 | (1) |
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8.4.6 Combiners Trained on Class Predictions |
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380 | (2) |
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8.4.7 Stacked Generalisation |
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382 | (1) |
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382 | (3) |
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385 | (2) |
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387 | (2) |
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389 | (1) |
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390 | (6) |
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8.4.13 Summary of Methods |
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396 | (2) |
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8.4.14 Example Application Study |
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398 | (1) |
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8.4.15 Further Developments |
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399 | (1) |
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399 | (1) |
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8.6 Summary and Discussion |
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400 | (1) |
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401 | (1) |
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401 | (1) |
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402 | (2) |
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404 | (29) |
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404 | (1) |
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9.2 Performance Assessment |
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405 | (19) |
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9.2.1 Performance Measures |
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405 | (1) |
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406 | (7) |
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413 | (2) |
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9.2.4 ROC Curves for Performance Assessment |
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415 | (4) |
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9.2.5 Population and Sensor Drift |
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419 | (2) |
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9.2.6 Example Application Study |
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421 | (1) |
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9.2.7 Further Developments |
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422 | (1) |
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423 | (1) |
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9.3 Comparing Classifier Performance |
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424 | (5) |
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9.3.1 Which Technique is Best? |
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424 | (1) |
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425 | (1) |
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9.3.3 Comparing Rules When Misclassification Costs are Uncertain |
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426 | (2) |
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9.3.4 Example Application Study |
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428 | (1) |
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9.3.5 Further Developments |
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429 | (1) |
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429 | (1) |
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429 | (1) |
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9.5 Summary and Discussion |
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430 | (1) |
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430 | (1) |
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430 | (1) |
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431 | (2) |
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10 Feature Selection and Extraction |
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433 | (68) |
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433 | (2) |
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435 | (28) |
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435 | (4) |
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10.2.2 Characterisation of Feature Selection Approaches |
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439 | (1) |
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10.2.3 Evaluation Measures |
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440 | (9) |
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10.2.4 Search Algorithms for Feature Subset Selection |
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449 | (1) |
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10.2.5 Complete Search - Branch and Bound |
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450 | (4) |
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454 | (4) |
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458 | (1) |
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459 | (1) |
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10.2.9 Stability of Feature Selection |
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460 | (2) |
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10.2.10 Example Application Study |
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462 | (1) |
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10.2.11 Further Developments |
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462 | (1) |
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463 | (1) |
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10.3 Linear Feature Extraction |
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463 | (21) |
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10.3.1 Principal Components Analysis |
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464 | (11) |
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10.3.2 Karhunen-Loeve Transformation |
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475 | (6) |
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10.3.3 Example Application Study |
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481 | (1) |
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10.3.4 Further Developments |
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482 | (1) |
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483 | (1) |
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10.4 Multidimensional Scaling |
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484 | (9) |
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484 | (2) |
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486 | (1) |
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487 | (3) |
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490 | (1) |
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10.4.5 MDS for Feature Extraction |
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491 | (1) |
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10.4.6 Example Application Study |
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492 | (1) |
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10.4.7 Further Developments |
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493 | (1) |
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493 | (1) |
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493 | (2) |
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10.6 Summary and Discussion |
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495 | (1) |
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495 | (1) |
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10.8 Notes and References |
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496 | (1) |
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497 | (4) |
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501 | (54) |
|
|
501 | (1) |
|
11.2 Hierarchical Methods |
|
|
502 | (8) |
|
11.2.1 Single-Link Method |
|
|
503 | (3) |
|
11.2.2 Complete-Link Method |
|
|
506 | (1) |
|
11.2.3 Sum-of-Squares Method |
|
|
507 | (1) |
|
11.2.4 General Agglomerative Algorithm |
|
|
508 | (1) |
|
11.2.5 Properties of a Hierarchical Classification |
|
|
508 | (1) |
|
11.2.6 Example Application Study |
|
|
509 | (1) |
|
|
509 | (1) |
|
|
510 | (1) |
|
|
511 | (2) |
|
|
511 | (1) |
|
11.4.2 Example Application Study |
|
|
512 | (1) |
|
11.5 Sum-of-Squares Methods |
|
|
513 | (18) |
|
11.5.1 Clustering Criteria |
|
|
514 | (1) |
|
11.5.2 Clustering Algorithms |
|
|
515 | (5) |
|
11.5.3 Vector Quantisation |
|
|
520 | (10) |
|
11.5.4 Example Application Study |
|
|
530 | (1) |
|
11.5.5 Further Developments |
|
|
530 | (1) |
|
|
531 | (1) |
|
|
531 | (7) |
|
11.6.1 Elementary Graph Theory |
|
|
531 | (3) |
|
11.6.2 Similarity Matrices |
|
|
534 | (1) |
|
11.6.3 Application to Clustering |
|
|
534 | (1) |
|
11.6.4 Spectral Clustering Algorithm |
|
|
535 | (1) |
|
11.6.5 Forms of Graph Laplacian |
|
|
535 | (1) |
|
11.6.6 Example Application Study |
|
|
536 | (2) |
|
11.6.7 Further Developments |
|
|
538 | (1) |
|
|
538 | (1) |
|
|
538 | (8) |
|
|
538 | (1) |
|
|
539 | (1) |
|
11.7.3 Absence of Class Structure |
|
|
540 | (1) |
|
11.7.4 Validity of Individual Clusters |
|
|
541 | (1) |
|
11.7.5 Hierarchical Clustering |
|
|
542 | (1) |
|
11.7.6 Validation of Individual Clusterings |
|
|
542 | (1) |
|
|
543 | (1) |
|
|
543 | (2) |
|
11.7.9 Choosing the Number of Clusters |
|
|
545 | (1) |
|
|
546 | (3) |
|
11.9 Summary and Discussion |
|
|
549 | (2) |
|
|
551 | (1) |
|
11.11 Notes and References |
|
|
552 | (1) |
|
|
553 | (2) |
|
|
555 | (26) |
|
|
555 | (6) |
|
|
557 | (1) |
|
|
557 | (2) |
|
12.1.3 Questions to Address |
|
|
559 | (1) |
|
12.1.4 Descriptive Features |
|
|
560 | (1) |
|
|
560 | (1) |
|
12.2 Mathematics of Networks |
|
|
561 | (4) |
|
|
561 | (1) |
|
|
562 | (1) |
|
|
562 | (1) |
|
|
563 | (1) |
|
12.2.5 Centrality Measures |
|
|
563 | (1) |
|
|
564 | (1) |
|
|
565 | (10) |
|
12.3.1 Clustering Methods |
|
|
565 | (3) |
|
12.3.2 Girvan-Newman Algorithm |
|
|
568 | (2) |
|
12.3.3 Modularity Approaches |
|
|
570 | (1) |
|
|
571 | (2) |
|
12.3.5 Clique Percolation |
|
|
573 | (1) |
|
12.3.6 Example Application Study |
|
|
574 | (1) |
|
12.3.7 Further Developments |
|
|
575 | (1) |
|
|
575 | (1) |
|
|
575 | (4) |
|
12.4.1 Approaches to Link Prediction |
|
|
576 | (2) |
|
12.4.2 Example Application Study |
|
|
578 | (1) |
|
12.4.3 Further Developments |
|
|
578 | (1) |
|
|
579 | (1) |
|
12.6 Summary and Discussion |
|
|
579 | (1) |
|
|
580 | (1) |
|
12.8 Notes and References |
|
|
580 | (1) |
|
|
580 | (1) |
|
|
581 | (10) |
|
|
581 | (4) |
|
13.1.1 Separate Training and Test Sets |
|
|
582 | (1) |
|
|
582 | (1) |
|
13.1.3 The Bayesian Viewpoint |
|
|
583 | (1) |
|
13.1.4 Akaike's Information Criterion |
|
|
583 | (1) |
|
13.1.5 Minimum Description Length |
|
|
584 | (1) |
|
|
585 | (1) |
|
13.3 Outlier Detection and Robust Procedures |
|
|
586 | (1) |
|
13.4 Mixed Continuous and Discrete Variables |
|
|
587 | (1) |
|
13.5 Structural Risk Minimisation and the Vapnik-Chervonenkis Dimension |
|
|
588 | (3) |
|
13.5.1 Bounds on the Expected Risk |
|
|
588 | (1) |
|
|
589 | (2) |
References |
|
591 | (46) |
Index |
|
637 | |