Optimal Reduced Rank Modeling, Prediction, Monitoring and Control using Canonical Variate Analysis

It is shown that for multivariate regression, CVA is a maximum likelihood method for determining the rank of such a relationship and has optimal statistical properties in terms of prediction accuracy and testing hypotheses not shared by PLS and PCA.

Abstract

Reduced rank methods such as partial least squares (PLS), principal component analysis (PCA), and canonical variate analysis (CVA), offer methods to determine economical models of relationships between process variables. It is shown that for multivariate regression, CVA is a maximum likelihood method for determining the rank of such a relationship. As a result CVA has optimal statistical properties in terms of prediction accuracy and testing hypotheses not shared by PLS and PCA. The extension of CVA to system identification of dynamical processes that gives optimal selection of the process state order is discussed. The use of CVA in process monitoring is developed for detecting process changes. Applications to chemical processes and particularly to a continuous stirred tank reactor for system identification, monitoring and control is discussed.