Eigenproblems in Pattern Recognition

Abstract

The task of studying the properties of configurations of points embedded in a metric space has long been a central task in pattern recognition, but has acquired even greater importance after the recent introduction of kernel- based learning methods. These methods work by virtually embedding general types of data in a vector space, and then analyzing the properties of the resulting data cloud. While a number of techniques for this task have been developed in fields as diverse as multivariate statistics, neural networks, and signal processing, many of them show an underlying unity. In this chapter we describe a large class of pattern analysis methods based on the use of generalized eigenproblems, which reduce to solving the equation Aw = λBw with respect to w and λ.