^ Springer. Computational Intelligence. A Methodological Introduction. Rudolf Kruse Christian Borgelt. Matthias Steinbrecher Pascal Held

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1 Rudolf Kruse Christian Borgelt Frank Klawonn Christian Moewes Matthias Steinbrecher Pascal Held Computational Intelligence A Methodological Introduction ^ Springer

2 Contents 1 Introduction Intelligent Systems Computational Intelligence About This Book 4 References 4 Part I Neural Networks 2 Introduction Motivation Biological Background 11 References 13 3 Threshold Logic Units Definition and Examples Geometric Interpretation Limitations Networks of Threshold Logic Units Training the Parameters Variants Training Networks 33 References 34 4 General Neural Networks Structure of Neural Networks Operation of Neural Networks Training Neural Networks 44 5 Multi-Layer Perceptrons Definition and Examples Function Approximation Logistic Regression Gradient Descent 62 vii

3 viij Contents 5.5 Error Backpropagation Gradient Descent Examples Variants of Gradient Descent Examples for Some Variants Sensitivity Analysis 80 References 81 6 Radial Basis Function Networks Definition and Examples Function Approximation Initializing the Parameters Training the Parameters Generalized Form 102 References Self-organizing Maps Definition and Examples Learning Vector Quantization Neighborhood of the Output Neurons 115 References Hopfield Networks Definition and Examples Convergence of the Computations Associative Memory Solving Optimization Problems Simulated Annealing 140 References Recurrent Networks Simple Examples Representing Differential Equations Vectorial Neural Networks Error Backpropagation in Time 154 References Mathematical Remarks Equations for Straight Lines Regression Activation Transformation 163 References 164 Part II Evolutionary Algorithms 11 Introduction to Evolutionary Algorithms Metaheuristics Biological Evolution Simulated Evolution 173

4 Contents ix 11.4 The n -Queens Problem Related Optimization Techniques The Traveling Salesman Problem 191 References Elements of Evolutionary Algorithms Encoding of Solution Candidates Fitness and Selection Genetic Operators 216 References Fundamental Evolutionary Algorithms Genetic Algorithms Evolution Strategies Genetic Programming Other Population-Based Approaches 262 References Special Applications and Techniques Behavioral Simulation Multi-criteria Optimization Parallelization 288 References 291 Part III Fuzzy Systems 15 Fuzzy Sets and Fuzzy Logic Natural Languages and Formal Models Fuzziness versus Uncertainty Fuzzy Sets Representation of Fuzzy Sets Fuzzy Logic Operations on Fuzzy Sets 314 References The Extension Principle Mappings of Fuzzy Sets Mapping of Level Sets Cartesian Product and Cylindrical Extension Extension Principle for Multivariate Mappings 326 References Fuzzy Relations Crisp Relations Application of Relations and Deduction Chains of Deductions Simple Fuzzy Relations Composition of Fuzzy Relations 338

5 x Contents 18 Similarity Relations Similarity Fuzzy Sets and Extensional Hulls Scaling Concepts Interpretation of Fuzzy Sets Possibility Theory 351 References Fuzzy Control Mamdani Controllers 353 Controllers Takagi-Sugeno-Kang 19.3 Logic-Based Controllers Mamdani Controller and Similarity Relations Hybrid Systems to Tune Fuzzy Controllers 370 References Fuzzy Clustering Fuzzy Methods in Data Analysis Clustering Presuppositions and Notation Classical c-means Clustering Fuzzification by Membership Transformation Fuzzification by Membership Regularization Comparison 402 References 403 Part IV Bayes Networks 21 Introduction to Bayes Networks A Fictitious Example Elements of Probability and Graph Theory Probability Theory Graph Theory 423 References Decompositions Dependence Graphs and Independence Graphs A Real-World Application 452 References Evidence Propagation Initialization Message Passing Update Marginalization Derivation Other Propagation Algorithms 467 References 467

6 Contents xi 25 Learning Graphical Models 469 References 477 Index 479

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