Principal Component Analysis for Multivariate Extremes

Background on Principal Component Analysis Principal component analysis (PCA) is a method widely used by practitioners for learning features of high-dimensional data [15]. It is a dimension reduction technique that represents the data in lower dimensions, often with the aim of exploratory analysis or visualization. PCA can also be used as a data preprocessing step, for instance in regression analysis. While PCA is familiar and commonplace for understanding behavior in the data's'bulk', only recently have similar methods been proposed for understanding high-dimensional extremes. The aim of this chapter is to review and compare recent approaches for extremal PCA. 1