Partial Least Squares

Abstract

Partial Least Squares (PLS), also known as Projection to Latent Structures, is a dimensionality reduction technique for maximizing the covariance between the predictor (independent) matrix X and the predicted (dependent) matrix Y for each component of the reduced space [61, 235]. A popular application of PLS is to select the matrix Y to contain only product quality data which can even include off-line measurement data, and the matrix X to contain all other process variables [144]. Such inferential models (also known as soft sensors) can be used for the on-line prediction of the product quality data [149, 155, 156], for incorporation into process control algorithms [106, 181, 182], as well as for process monitoring [144, 181, 182]. Discriminant PLS selects the matrix X to contain all process variables and selects the Y matrix to focus PLS on the task of fault diagnosis [26].