Principal component analysis

Abstract

This chapter discusses the use of principal component analysis (PCA) for analyzing high-dimensional data in the context of brain disorders. PCA belongs to the family of dimension reduction methods and is particularly useful when the data are large (i.e., multiple variables), big (i.e., multiple observations per variable), and highly correlated. The goal is to identify a reduced set of features that represent the original data in a lower-dimensional subspace with minimal loss of information. PCA and related methods provide means to summarize the data and extract information about individual differences. This makes these methods particularly useful in the era of Big Data and personalized medicine. In the first section, we explain the mathematical formula behind PCA. In the second section, we show how to implement the method using a toy example. Finally, in the last section, we discuss some exemplar applications of PCA from the existing literature.