Nonlinear Modeling

1 Neural Nets and Related Model Structures for Nonlinear System Identification.- 1.1 Introduction.- 1.2 Black-box Identification Approach.- 1.3 Fitting the Parameters.- 1.4 The Nonlinear Mapping.- 1.5 Some Standard Theory on Model Properties.- 1.6 Bias-Variance Trade-off.- 1.7 Discussion.- 1.8 Dynamic Systems.- 1.9 A stepwise Approach to Nonlinear Black-box Identification.- 1.10 Examples.- 1.11 Conclusions.- References.- 2 Enhanced Multi-Stream Kaiman Filter Training for Recurrent Networks.- 2.1 Introduction.- 2.2 Network Architecture and Execution.- 2.3 Gradient Calculation.- 2.4 EKF Multi-Stream Training.- 2.5 A Modeling Example.- 2.6 Alternating training of weights and initial states.- 2.7 Toward more coordinated training of weights and states-A Motivating Example.- 2.8 The Mackey-Glass Series.- 2.9 Use of a structured evolver.- 2.10 Summary.- References.- 3 The Support Vector Method of Function Estimation.- 3.1 Introduction.- 3.2 The Optimal Hyperplane.- 3.3 The Support Vector Machine for Pattern Recognition.- 3.4 Examples of SV Machines for Pattern Recognition.- 3.5 The SVM for regression estimation.- 3.6 Kernels for Estimating Real-Valued Functions.- 3.7 Solving Operator Equations.- 3.8 Conclusion.- References.- 4 Parametric Density Estimation for the Classification of Acoustic Feature Vectors in Speech Recognition.- 4.1 Introduction.- 4.2 The Probability Densities.- 4.3 Maximum Likelihood Estimation.- 4.4 Mixture Models.- 4.5 Numerical experiment.- 4.6 Conclusion.- References.- 5 Wavelet Based Modeling of Nonlinear Systems.- 5.1 Introduction.- 5.2 Wavelet Interpolation Method.- 5.3 Wavelet Interpolation in Sobolev Space.- 5.4 Numerical Examples.- 5.5 Conclusions.- Appendix: Constrained Minimal Norm Interpolation.- References.- 6 Nonlinear Identification based onFuzzy Models.- 6.1 Introduction.- 6.2 Functional fuzzy models.- 6.3 Fuzzy Modelling algorithms without structure determination.- 6.4 Structure determination.- 6.5 A worked example.- 6.6 Discussion.-