Partial least squares: application in classification and multivariable process dynamics identification

Abstract

Projection to latent structures or partial least squares (PLS) is a multivariable statistical regression method based on projecting/viewing the information in a high-dimensional data space down onto a low dimensional one defined by some latent variables. PLS is successfully applied in diverse fields including process monitoring; identification of process dynamics & control and deals with noisy and highly correlated data, quite often, only with a limited number of observations available. The conventional PLS is suitable for modeling time independent or steady state processes. For modeling dynamic process, the input data matrix (X) is augmented either with large number of lagged input variables (called finite impulse response (FIR) model) or including lagged input and output variables (called auto regressive model with exogenous input, ARX). By combining the PLS with ARX and FIR model structure, non-linear dynamic processes can be modeled. In the present study, PLS algorithm was used for wine classification and identification of the dynamics of a MIMO process. In the present work, 178 numbers of wine samples possessing 13 number of feature variables were successfully classified using PLS method with minor isclassifications. Before classification the supervised non- hierarchical K-means clustering was used to designate the classes available among the wine samples, hence discrimination. The efficiency of PLS based classifier was compared with those based on unsupervised neural network ART1 (Adaptive Resonance Theory) and supervised neural network PNN (Probabilistic neural network). In the present work, a non-linear MIMO distillation process (4×4) was identified with reasonable accuracy along with the evaluation of input-output loading matrix which would logically build up the framework for PLS based process controller. The ARX models as well as least squares were used to build up inner relations among the scores. MIMO processes were casted as a series of SISO identification problems.