Chapter 1 - Data Fitting with Linear Models

1.1 Introduction

1.2 Linear Models

1.3 Least Squares

1.4 Adaptive Linear Systems

1.5 Estimation of the Gradient: The LMS Algorithm

1.6 A Methodology for Stable Adaptation

1.7 Regression for Multiple Variables

1.8 Newton's Method

1.9 Analytic versus Iterative Solutions

1.10 The Linear Regression Model

1.11 Conclusions

1.12 Exercises

1.13 NeuroSolutions Examples

1.14 Concept Map for Chapter 1

The goal of this chapter is to introduce the following concepts:

· Data fitting and the derivation of the best linear (regression) model

· Iterative solution of the regression model

· Steepest descent methods

· The least mean square (LMS) estimator for the gradient

· The trade-off between speed of adaptation and solution accuracy

· Examples using NeuroSolutions

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