THE GEOMETRY OF 2-BLOCK PARTIAL LEAST-SQUARES REGRESSION

In this paper, we outline a geometric interpretation of both univariate and multivariate partial least squares regression (PLS) that illustrates very clearly the mathematical description of the PLS algorithms. In addition, we show how the concept of continuum regression arises quite naturally out of a geometric interpretation of ordinary least squares, principal component regression, and PLS. We also derive a simple expression that relates the first PLS dimension to the correlational- and eigen-structure of the data and suggest a property of PLS subspaces as a whole, one that is defined with respect to the corresponding subspace in principal component regression.