Principal Component Analysis (PCA)

Synonyms

Eigen decomposition; Latent factor analysis; Singular value decomposition (SVD)

Definition

PCA is a statistical tool used to explore complex series of multivariate observations by which we can summarize a great amount of data through recognition of its most relevant information content. PCA behaves as a filtering-compression technique that captures the main trends in the data while revealing their underlying structure (Johnson and Wichner 1998; Brereton 2003; Wall et al. 2003).

Characteristics

Motivation Problem

When in a set of n “objects” (the experimental units) m attributes are measured, a cloud of points would appear when objects are represented in a space where each axis corresponds to one variable. PCA focuses on the “shape” of such cloud, trying to capture the cloud’s dominating directions(the eigenvectors). When these data are projected onto a lower-dimensional subspace, delimited by the eigenvectors of the cloud, a clearer visualization of the relationship between...