Principal Component Analysis and Extensions

Abstract

This chapter introduces principal component analysis (PCA), a technique for dimension reduction in multivariate datasets. At its core there is a matrix decomposition technique called singular value decomposition, which is introduced at the beginning of this chapter. This is followed by PCA model formulation, computation, and an application. Relationships with exploratory factor analysis are discussed as well. Subsequently, some PCA variants such as robust and sparse PCA are briefly discussed. The final two sections introduce two extensions of PCA. The first one is three-way PCA for three-way input data structures. The second one is called independent component analysis and illustrated using electroencephalography (EEG) data.