12 - Principal Component Analysis

Summary

Large data sets are difficult to grasp. To make progress, we often seek a few quantities that capture as much of the information in the data as possible. In this chapter, we discuss a procedure called Principal Component Analysis (PCA), also called Empirical Orthogonal Function (EOF) analysis, which finds the components that minimizes the sum square difference between the components and the data. The components are ordered such that the first approximates the data the best (in a least squares sense), the second approximates the data the best among all components orthogonal to the first, and so on. In typical climate applications, a principal component consists of two parts: (1) a fixed spatial structure, called an Empirical Orthogonal Function (EOF), and (2) its time-dependent amplitude, called a PC time series. The EOFs are orthogonal and the PC time series are uncorrelated. Principal components often are used as input to other analyses, such as linear regression, canonical correlation analysis, predictable components analysis, or discriminant analysis. The procedure for performing area-weighted PCA is discussed in detail in this chapter.