{"product_id":"combining-pattern-classifiers-isbn-9781118315231","title":"Combining Pattern Classifiers","description":"\u003cb\u003eA unified, coherent treatment of current classifier ensemble methods, from fundamentals of pattern recognition to ensemble feature selection, now in its second edition\u003c\/b\u003e \u003cp\u003eThe art and science of combining pattern classifiers has flourished into a prolific discipline since the first edition of \u003ci\u003eCombining Pattern Classifiers\u003c\/i\u003e was published in 2004. Dr. Kuncheva has plucked from the rich landscape of recent classifier ensemble literature the topics, methods, and algorithms that will guide the reader toward a deeper understanding of the fundamentals, design, and applications of classifier ensemble methods.\u003c\/p\u003e \u003cp\u003eThoroughly updated, with MATLAB® code and practice data sets throughout, \u003ci\u003eCombining Pattern Classifiers\u003c\/i\u003e includes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eCoverage of Bayes decision theory and experimental comparison of classifiers\u003c\/li\u003e \u003cli\u003eEssential ensemble methods such as Bagging, Random forest, AdaBoost, Random subspace, Rotation forest, Random oracle, and Error Correcting Output Code, among others\u003c\/li\u003e \u003cli\u003eChapters on classifier selection, diversity, and ensemble feature selection\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eWith firm grounding in the fundamentals of pattern recognition, and featuring more than 140 illustrations, \u003ci\u003eCombining Pattern Classifiers, Second Edition\u003c\/i\u003e is a valuable reference for postgraduate students, researchers, and practitioners in computing and engineering.\u003c\/p\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eAcknowledgements xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Fundamentals of Pattern Recognition 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Basic Concepts: Class, Feature, Data Set 1\u003c\/p\u003e \u003cp\u003e1.1.1 Classes and Class Labels 1\u003c\/p\u003e \u003cp\u003e1.1.2 Features 2\u003c\/p\u003e \u003cp\u003e1.1.3 Data Set 3\u003c\/p\u003e \u003cp\u003e1.1.4 Generate Your Own Data 6\u003c\/p\u003e \u003cp\u003e1.2 Classifier, Discriminant Functions, Classification Regions 9\u003c\/p\u003e \u003cp\u003e1.3 Classification Error and Classification Accuracy 11\u003c\/p\u003e \u003cp\u003e1.3.1 Where Does the Error Come From? Bias and Variance 11\u003c\/p\u003e \u003cp\u003e1.3.2 Estimation of the Error 13\u003c\/p\u003e \u003cp\u003e1.3.3 Confusion Matrices and Loss Matrices 14\u003c\/p\u003e \u003cp\u003e1.3.4 Training and Testing Protocols 15\u003c\/p\u003e \u003cp\u003e1.3.5 Overtraining and Peeking 17\u003c\/p\u003e \u003cp\u003e1.4 Experimental Comparison of Classifiers 19\u003c\/p\u003e \u003cp\u003e1.4.1 Two Trained Classifiers and a Fixed Testing Set 20\u003c\/p\u003e \u003cp\u003e1.4.2 Two Classifier Models and a Single Data Set 22\u003c\/p\u003e \u003cp\u003e1.4.3 Two Classifier Models and Multiple Data Sets 26\u003c\/p\u003e \u003cp\u003e1.4.4 Multiple Classifier Models and Multiple Data Sets 27\u003c\/p\u003e \u003cp\u003e1.5 Bayes Decision Theory 30\u003c\/p\u003e \u003cp\u003e1.5.1 Probabilistic Framework 30\u003c\/p\u003e \u003cp\u003e1.5.2 Discriminant Functions and Decision Boundaries 31\u003c\/p\u003e \u003cp\u003e1.5.3 Bayes Error 33\u003c\/p\u003e \u003cp\u003e1.6 Clustering and Feature Selection 35\u003c\/p\u003e \u003cp\u003e1.6.1 Clustering 35\u003c\/p\u003e \u003cp\u003e1.6.2 Feature Selection 37\u003c\/p\u003e \u003cp\u003e1.7 Challenges of Real-Life Data 40\u003c\/p\u003e \u003cp\u003eAppendix 41\u003c\/p\u003e \u003cp\u003e1.A.1 Data Generation 41\u003c\/p\u003e \u003cp\u003e1.A.2 Comparison of Classifiers 42\u003c\/p\u003e \u003cp\u003e1.A.2.1 MATLAB Functions for Comparing Classifiers 42\u003c\/p\u003e \u003cp\u003e1.A.2.2 Critical Values for Wilcoxon and Sign Test 45\u003c\/p\u003e \u003cp\u003e1.A.3 Feature Selection 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Base Classifiers 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Linear and Quadratic Classifiers 49\u003c\/p\u003e \u003cp\u003e2.1.1 Linear Discriminant Classifier 49\u003c\/p\u003e \u003cp\u003e2.1.2 Nearest Mean Classifier 52\u003c\/p\u003e \u003cp\u003e2.1.3 Quadratic Discriminant Classifier 52\u003c\/p\u003e \u003cp\u003e2.1.4 Stability of LDC and QDC 53\u003c\/p\u003e \u003cp\u003e2.2 Decision Tree Classifiers 55\u003c\/p\u003e \u003cp\u003e2.2.1 Basics and Terminology 55\u003c\/p\u003e \u003cp\u003e2.2.2 Training of Decision Tree Classifiers 57\u003c\/p\u003e \u003cp\u003e2.2.3 Selection of the Feature for a Node 58\u003c\/p\u003e \u003cp\u003e2.2.4 Stopping Criterion 60\u003c\/p\u003e \u003cp\u003e2.2.5 Pruning of the Decision Tree 63\u003c\/p\u003e \u003cp\u003e2.2.6 C4.5 and ID3 64\u003c\/p\u003e \u003cp\u003e2.2.7 Instability of Decision Trees 64\u003c\/p\u003e \u003cp\u003e2.2.8 Random Trees 65\u003c\/p\u003e \u003cp\u003e2.3 The Naïve Bayes Classifier 66\u003c\/p\u003e \u003cp\u003e2.4 Neural Networks 68\u003c\/p\u003e \u003cp\u003e2.4.1 Neurons 68\u003c\/p\u003e \u003cp\u003e2.4.2 Rosenblatt’s Perceptron 70\u003c\/p\u003e \u003cp\u003e2.4.3 Multi-Layer Perceptron 71\u003c\/p\u003e \u003cp\u003e2.5 Support Vector Machines 73\u003c\/p\u003e \u003cp\u003e2.5.1 Why Would It Work? 73\u003c\/p\u003e \u003cp\u003e2.5.2 Classification Margins 74\u003c\/p\u003e \u003cp\u003e2.5.3 Optimal Linear Boundary 76\u003c\/p\u003e \u003cp\u003e2.5.4 Parameters and Classification Boundaries of SVM 78\u003c\/p\u003e \u003cp\u003e2.6 The \u003ci\u003ek\u003c\/i\u003e-Nearest Neighbor Classifier (\u003ci\u003ek\u003c\/i\u003e-nn) 80\u003c\/p\u003e \u003cp\u003e2.7 Final Remarks 82\u003c\/p\u003e \u003cp\u003e2.7.1 Simple or Complex Models? 82\u003c\/p\u003e \u003cp\u003e2.7.2 The Triangle Diagram 83\u003c\/p\u003e \u003cp\u003e2.7.3 Choosing a Base Classifier for Ensembles 85\u003c\/p\u003e \u003cp\u003eAppendix 85\u003c\/p\u003e \u003cp\u003e2.A.1 MATLAB Code for the Fish Data 85\u003c\/p\u003e \u003cp\u003e2.A.2 MATLAB Code for Individual Classifiers 86\u003c\/p\u003e \u003cp\u003e2.A.2.1 Decision Tree 86\u003c\/p\u003e \u003cp\u003e2.A.2.2 Naïve Bayes 89\u003c\/p\u003e \u003cp\u003e2.A.2.3 Multi-Layer Perceptron 90\u003c\/p\u003e \u003cp\u003e2.A.2.4 1-nn Classifier 92\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 An Overview of the Field 94\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Philosophy 94\u003c\/p\u003e \u003cp\u003e3.2 Two Examples 98\u003c\/p\u003e \u003cp\u003e3.2.1 The Wisdom of the “Classifier Crowd” 98\u003c\/p\u003e \u003cp\u003e3.2.2 The Power of Divide-and-Conquer 98\u003c\/p\u003e \u003cp\u003e3.3 Structure of the Area 100\u003c\/p\u003e \u003cp\u003e3.3.1 Terminology 100\u003c\/p\u003e \u003cp\u003e3.3.2 A Taxonomy of Classifier Ensemble Methods 100\u003c\/p\u003e \u003cp\u003e3.3.3 Classifier Fusion and Classifier Selection 104\u003c\/p\u003e \u003cp\u003e3.4 Quo Vadis? 105\u003c\/p\u003e \u003cp\u003e3.4.1 Reinventing the Wheel? 105\u003c\/p\u003e \u003cp\u003e3.4.2 The Illusion of Progress? 106\u003c\/p\u003e \u003cp\u003e3.4.3 A Bibliometric Snapshot 107\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Combining Label Outputs 111\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Types of Classifier Outputs 111\u003c\/p\u003e \u003cp\u003e4.2 A Probabilistic Framework for Combining Label Outputs 112\u003c\/p\u003e \u003cp\u003e4.3 Majority Vote 113\u003c\/p\u003e \u003cp\u003e4.3.1 “Democracy” in Classifier Combination 113\u003c\/p\u003e \u003cp\u003e4.3.2 Accuracy of the Majority Vote 114\u003c\/p\u003e \u003cp\u003e4.3.3 Limits on the Majority Vote Accuracy: An Example 117\u003c\/p\u003e \u003cp\u003e4.3.4 Patterns of Success and Failure 119\u003c\/p\u003e \u003cp\u003e4.3.5 Optimality of the Majority Vote Combiner 124\u003c\/p\u003e \u003cp\u003e4.4 Weighted Majority Vote 125\u003c\/p\u003e \u003cp\u003e4.4.1 Two Examples 126\u003c\/p\u003e \u003cp\u003e4.4.2 Optimality of the Weighted Majority Vote Combiner 127\u003c\/p\u003e \u003cp\u003e4.5 Naïve-Bayes Combiner 128\u003c\/p\u003e \u003cp\u003e4.5.1 Optimality of the Naïve Bayes Combiner 128\u003c\/p\u003e \u003cp\u003e4.5.2 Implementation of the NB Combiner 130\u003c\/p\u003e \u003cp\u003e4.6 Multinomial Methods 132\u003c\/p\u003e \u003cp\u003e4.7 Comparison of Combination Methods for Label Outputs 135\u003c\/p\u003e \u003cp\u003eAppendix 137\u003c\/p\u003e \u003cp\u003e4.A.1 Matan’s Proof for the Limits on the Majority Vote Accuracy 137\u003c\/p\u003e \u003cp\u003e4.A.2 Selected MATLAB Code 139\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Combining Continuous-Valued Outputs 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Decision Profile 143\u003c\/p\u003e \u003cp\u003e5.2 How Do We Get Probability Outputs? 144\u003c\/p\u003e \u003cp\u003e5.2.1 Probabilities Based on Discriminant Scores 144\u003c\/p\u003e \u003cp\u003e5.2.2 Probabilities Based on Counts: Laplace Estimator 147\u003c\/p\u003e \u003cp\u003e5.3 Nontrainable (Fixed) Combination Rules 150\u003c\/p\u003e \u003cp\u003e5.3.1 A Generic Formulation 150\u003c\/p\u003e \u003cp\u003e5.3.2 Equivalence of Simple Combination Rules 152\u003c\/p\u003e \u003cp\u003e5.3.3 Generalized Mean Combiner 153\u003c\/p\u003e \u003cp\u003e5.3.4 A Theoretical Comparison of Simple Combiners 156\u003c\/p\u003e \u003cp\u003e5.3.5 Where Do They Come From? 160\u003c\/p\u003e \u003cp\u003e5.4 The Weighted Average (Linear Combiner) 166\u003c\/p\u003e \u003cp\u003e5.4.1 Consensus Theory 166\u003c\/p\u003e \u003cp\u003e5.4.2 Added Error for the Weighted Mean Combination 167\u003c\/p\u003e \u003cp\u003e5.4.3 Linear Regression 168\u003c\/p\u003e \u003cp\u003e5.5 A Classifier as a Combiner 172\u003c\/p\u003e \u003cp\u003e5.5.1 The Supra Bayesian Approach 172\u003c\/p\u003e \u003cp\u003e5.5.2 Decision Templates 173\u003c\/p\u003e \u003cp\u003e5.5.3 A Linear Classifier 175\u003c\/p\u003e \u003cp\u003e5.6 An Example of Nine Combiners for Continuous-Valued Outputs 175\u003c\/p\u003e \u003cp\u003e5.7 To Train or Not to Train? 176\u003c\/p\u003e \u003cp\u003eAppendix 178\u003c\/p\u003e \u003cp\u003e5.A.1 Theoretical Classification Error for the Simple Combiners 178\u003c\/p\u003e \u003cp\u003e5.A.1.1 Set-up and Assumptions 178\u003c\/p\u003e \u003cp\u003e5.A.1.2 Individual Error 180\u003c\/p\u003e \u003cp\u003e5.A.1.3 Minimum and Maximum 180\u003c\/p\u003e \u003cp\u003e5.A.1.4 Average (Sum) 181\u003c\/p\u003e \u003cp\u003e5.A.1.5 Median and Majority Vote 182\u003c\/p\u003e \u003cp\u003e5.A.1.6 Oracle 183\u003c\/p\u003e \u003cp\u003e5.A.2 Selected MATLAB Code 183\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Ensemble Methods 186\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Bagging 186\u003c\/p\u003e \u003cp\u003e6.1.1 The Origins: Bagging Predictors 186\u003c\/p\u003e \u003cp\u003e6.1.2 Why Does Bagging Work? 187\u003c\/p\u003e \u003cp\u003e6.1.3 Out-of-bag Estimates 189\u003c\/p\u003e \u003cp\u003e6.1.4 Variants of Bagging 190\u003c\/p\u003e \u003cp\u003e6.2 Random Forests 190\u003c\/p\u003e \u003cp\u003e6.3 AdaBoost 192\u003c\/p\u003e \u003cp\u003e6.3.1 The AdaBoost Algorithm 192\u003c\/p\u003e \u003cp\u003e6.3.2 The arc-x4 Algorithm 194\u003c\/p\u003e \u003cp\u003e6.3.3 Why Does AdaBoost Work? 195\u003c\/p\u003e \u003cp\u003e6.3.4 Variants of Boosting 199\u003c\/p\u003e \u003cp\u003e6.3.5 A Famous Application: AdaBoost for Face Detection 199\u003c\/p\u003e \u003cp\u003e6.4 Random Subspace Ensembles 203\u003c\/p\u003e \u003cp\u003e6.5 Rotation Forest 204\u003c\/p\u003e \u003cp\u003e6.6 Random Linear Oracle 208\u003c\/p\u003e \u003cp\u003e6.7 Error Correcting Output Codes (ECOC) 211\u003c\/p\u003e \u003cp\u003e6.7.1 Code Designs 212\u003c\/p\u003e \u003cp\u003e6.7.2 Decoding 214\u003c\/p\u003e \u003cp\u003e6.7.3 Ensembles of Nested Dichotomies 216\u003c\/p\u003e \u003cp\u003eAppendix 218\u003c\/p\u003e \u003cp\u003e6.A.1 Bagging 218\u003c\/p\u003e \u003cp\u003e6.A.2 AdaBoost 220\u003c\/p\u003e \u003cp\u003e6.A.3 Random Subspace 223\u003c\/p\u003e \u003cp\u003e6.A.4 Rotation Forest 225\u003c\/p\u003e \u003cp\u003e6.A.5 Random Linear Oracle 228\u003c\/p\u003e \u003cp\u003e6.A.6 ECOC 229\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Classifier Selection 230\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Preliminaries 230\u003c\/p\u003e \u003cp\u003e7.2 Why Classifier Selection Works 231\u003c\/p\u003e \u003cp\u003e7.3 Estimating Local Competence Dynamically 233\u003c\/p\u003e \u003cp\u003e7.3.1 Decision-Independent Estimates 233\u003c\/p\u003e \u003cp\u003e7.3.2 Decision-Dependent Estimates 238\u003c\/p\u003e \u003cp\u003e7.4 Pre-Estimation of the Competence Regions 239\u003c\/p\u003e \u003cp\u003e7.4.1 Bespoke Classifiers 240\u003c\/p\u003e \u003cp\u003e7.4.2 Clustering and Selection 241\u003c\/p\u003e \u003cp\u003e7.5 Simultaneous Training of Regions and Classifiers 242\u003c\/p\u003e \u003cp\u003e7.6 Cascade Classifiers 244\u003c\/p\u003e \u003cp\u003eAppendix: Selected MATLAB Code 244\u003c\/p\u003e \u003cp\u003e7.A.1 Banana Data 244\u003c\/p\u003e \u003cp\u003e7.A.2 Evolutionary Algorithm for a Selection Ensemble for the Banana Data 245\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Diversity in Classifier Ensembles 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 What is Diversity? 247\u003c\/p\u003e \u003cp\u003e8.1.1 Diversity for a Point-Value Estimate 248\u003c\/p\u003e \u003cp\u003e8.1.2 Diversity in Software Engineering 248\u003c\/p\u003e \u003cp\u003e8.1.3 Statistical Measures of Relationship 249\u003c\/p\u003e \u003cp\u003e8.2 Measuring Diversity in Classifier Ensembles 250\u003c\/p\u003e \u003cp\u003e8.2.1 Pairwise Measures 250\u003c\/p\u003e \u003cp\u003e8.2.2 Nonpairwise Measures 251\u003c\/p\u003e \u003cp\u003e8.3 Relationship Between Diversity and Accuracy 256\u003c\/p\u003e \u003cp\u003e8.3.1 An Example 256\u003c\/p\u003e \u003cp\u003e8.3.2 Relationship Patterns 258\u003c\/p\u003e \u003cp\u003e8.3.3 A Caveat: Independent Outputs ≠ Independent Errors 262\u003c\/p\u003e \u003cp\u003e8.3.4 Independence is Not the Best Scenario 265\u003c\/p\u003e \u003cp\u003e8.3.5 Diversity and Ensemble Margins 267\u003c\/p\u003e \u003cp\u003e8.4 Using Diversity 270\u003c\/p\u003e \u003cp\u003e8.4.1 Diversity for Finding Bounds and Theoretical Relationships 270\u003c\/p\u003e \u003cp\u003e8.4.2 Kappa-error Diagrams and Ensemble Maps 271\u003c\/p\u003e \u003cp\u003e8.4.3 Overproduce and Select 275\u003c\/p\u003e \u003cp\u003e8.5 Conclusions: Diversity of Diversity 279\u003c\/p\u003e \u003cp\u003eAppendix 280\u003c\/p\u003e \u003cp\u003e8.A.1 Derivation of Diversity Measures for Oracle Outputs 280\u003c\/p\u003e \u003cp\u003e8.A.1.1 Correlation \u003ci\u003e𝜌\u003c\/i\u003e 280\u003c\/p\u003e \u003cp\u003e8.A.1.2 Interrater Agreement \u003ci\u003e𝜅\u003c\/i\u003e 281\u003c\/p\u003e \u003cp\u003e8.A.2 Diversity Measure Equivalence 282\u003c\/p\u003e \u003cp\u003e8.A.3 Independent Outputs ≠ Independent Errors 284\u003c\/p\u003e \u003cp\u003e8.A.4 A Bound on the Kappa-Error Diagram 286\u003c\/p\u003e \u003cp\u003e8.A.5 Calculation of the Pareto Frontier 287\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Ensemble Feature Selection 290\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Preliminaries 290\u003c\/p\u003e \u003cp\u003e9.1.1 Right and Wrong Protocols 290\u003c\/p\u003e \u003cp\u003e9.1.2 Ensemble Feature Selection Approaches 294\u003c\/p\u003e \u003cp\u003e9.1.3 Natural Grouping 294\u003c\/p\u003e \u003cp\u003e9.2 Ranking by Decision Tree Ensembles 295\u003c\/p\u003e \u003cp\u003e9.2.1 Simple Count and Split Criterion 295\u003c\/p\u003e \u003cp\u003e9.2.2 Permuted Features or the “Noised-up” Method 297\u003c\/p\u003e \u003cp\u003e9.3 Ensembles of Rankers 299\u003c\/p\u003e \u003cp\u003e9.3.1 The Approach 299\u003c\/p\u003e \u003cp\u003e9.3.2 Ranking Methods (Criteria) 300\u003c\/p\u003e \u003cp\u003e9.4 Random Feature Selection for the Ensemble 305\u003c\/p\u003e \u003cp\u003e9.4.1 Random Subspace Revisited 305\u003c\/p\u003e \u003cp\u003e9.4.2 Usability, Coverage, and Feature Diversity 306\u003c\/p\u003e \u003cp\u003e9.4.3 Genetic Algorithms 312\u003c\/p\u003e \u003cp\u003e9.5 Nonrandom Selection 315\u003c\/p\u003e \u003cp\u003e9.5.1 The “Favorite Class” Model 315\u003c\/p\u003e \u003cp\u003e9.5.2 The Iterative Model 315\u003c\/p\u003e \u003cp\u003e9.5.3 The Incremental Model 316\u003c\/p\u003e \u003cp\u003e9.6 A Stability Index 317\u003c\/p\u003e \u003cp\u003e9.6.1 Consistency Between a Pair of Subsets 317\u003c\/p\u003e \u003cp\u003e9.6.2 A Stability Index for K Sequences 319\u003c\/p\u003e \u003cp\u003e9.6.3 An Example of Applying the Stability Index 320\u003c\/p\u003e \u003cp\u003eAppendix 322\u003c\/p\u003e \u003cp\u003e9.A.1 MATLAB Code for the Numerical Example of Ensemble Ranking 322\u003c\/p\u003e \u003cp\u003e9.A.2 MATLAB GA Nuggets 322\u003c\/p\u003e \u003cp\u003e9.A.3 MATLAB Code for the Stability Index 324\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 A Final Thought 326\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 327\u003c\/p\u003e \u003cp\u003eIndex 353\u003c\/p\u003e \u003cp\u003e\u003cb\u003eLudmila Kuncheva\u003c\/b\u003e is a Professor of Computer Science at Bangor University, United Kingdom. She has received two IEEE Best Paper awards. In 2012, Dr. Kuncheva was awarded a Fellowship to the International Association for Pattern Recognition (IAPR) for her contributions to multiple classifier systems.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eA unified, coherent treatment of current classifier ensemble methods, from fundamentals of pattern recognition to ensemble feature selection, now in its second edition\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe art and science of combining pattern classifiers has flourished into a prolific discipline since the first edition of \u003ci\u003eCombining Pattern Classifiers\u003c\/i\u003e was published in 2004. Dr. Kuncheva has plucked from the rich landscape of recent classifier ensemble literature the topics, methods, and algorithms that will guide the reader toward a deeper understanding of the fundamentals, design, and applications of classifier ensemble methods.\u003c\/p\u003e \u003cp\u003eThoroughly updated, with MATLAB® code and practice data sets throughout, \u003ci\u003eCombining Pattern Classifiers\u003c\/i\u003e includes:\u003c\/p\u003e \u003cp\u003e• Coverage of Bayes decision theory and experimental comparison of classifiers\u003c\/p\u003e \u003cp\u003e• Essential ensemble methods such as Bagging, Random forest, AdaBoost, Random subspace, Rotation forest, Random oracle, and Error Correcting Output Code, among others\u003c\/p\u003e \u003cp\u003e• Chapters on classifier selection, diversity, and ensemble feature selection\u003c\/p\u003e \u003cp\u003eWith firm grounding in the fundamentals of pattern recognition, and featuring more than 140 illustrations, \u003ci\u003eCombining Pattern Classifiers, Second Edition\u003c\/i\u003e is a valuable reference for postgraduate students, researchers, and practitioners in computing and engineering.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988948730085,"sku":"NP9781118315231","price":127.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118315231.jpg?v=1761782169","url":"https:\/\/k12savings.com\/products\/combining-pattern-classifiers-isbn-9781118315231","provider":"K12savings","version":"1.0","type":"link"}