Adaptive Signal Processing: Next Generation Solutions

6

NONLINEAR SEQUENTIAL STATE ESTIMATION FOR SOLVING PATTERN-CLASSIFICATION PROBLEMS

Simon Haykin and Ienkaran Arasaratnam

McMaster University, Canada

6.1 INTRODUCTION

Sequential state estimation has established itself as one of the essential elements of signal processing and control theory. Typically, we think of its use being confined to dynamic systems, where we are given a set of observables and the requirement is to estimate the hidden state of the system on which the observables are dependant. However, when the issue of interest is that of pattern-classification (recognition), we usually do not think of sequential estimation as a relevant tool for solving such problems. Perhaps, this oversight may be attributed to the fact that pattern-classification machines are usually viewed as static rather than dynamic systems. In this chapter, we take a different view: Specifically, we look to nonlinear sequential state estimation as a tool for solving pattern-classification problems, where the problem is solved through an iterative supervised learning process. In so doing, we demonstrate that this approach to solving pattern-classification problems offers several computational advantages compared to traditional methods, particularly when the problem of interest is difficult or large-scale.

The chapter is structured as follows: Section 6.2 briefly discusses the back-propagation (BP) algorithm and support-vector machine (SVM) learning as two commonly used procedures for pattern classification; ...