Chapter ? ? High - Dimensional Classification ∗

In this chapter, we give a comprehensive overview on high-dimensional classification, which is prominently featured in many contemporary statistical problems. Emphasis is given on the impact of dimensionality on implementation and statistical performance and on the feature selection to enhance statistical performance as well as scientific understanding between collected variables and the outcome. Penalized methods and independence learning are introduced for feature selection in ultrahigh dimensional feature space. Popular methods such as the Fisher linear discriminant, Bayes classifiers, independence rules and distance based classifiers and loss-based classification rules are introduced and their merits are critically examined. Extensions to multi-class problems are also given.