Non-linear partial least squares through data transformations

Abstract

Partial Least Squares (PLS) is one of the most frequently used techniques for process modelling and monitoring with correlated data. In this paper, a Box-Tidwell transformation based PLS algorithm (BTPLS) is proposed to deal with non-linear problems in complex systems. The BTPLS algorithm provides a family of flexible regression models for data fitting. These are shown to out-perform both the linear and quadratic PLS algorithms for non-linear problems in terms of modelling and prediction accuracy. In contrast to neural network based PLS (NNPLS) algorithms, the BTPLS algorithm significantly reduces computational costs and exhibits better performance for many practical situations in terms of Akaike Information Criterion. This is due to the resultant model forms being more parsimonious and the use of a non-iterative search for data transformations and regression coefficients. The BTPLS is a compromise between model simplicity and accuracy, and constitutes a complementary modelling technique alongside linear PLS and NNPLS.