Eigenproblems in Pattern Recognition
The task of studying the properties of conﬂgurations of points embeddedin a metric space has long been a central task in pattern recognition, buthas acquired even greater importance after the recent introduction of kernel-based learning methods. These methods work by virtually embedding generaltypes of data in a vector space, and then analyzing the properties of theresulting data cloud. While a number of techniques for this task have beendeveloped in ﬂelds as diverse as multivariate statistics, neural networks, andsignal processing, many of them show an underlying unity. In this chapterwe describe a large class of pattern analysis methods based on the use ofgeneralized eigenproblems, which reduce to solving the equation Aw =