(531a) Advances in Non-Linear Multivariate Latent Variable Regression Using Non-Linear Programming Methods

Multivariate latent variable regression models such as PCR and PLS are effective ways of dealing with massive amounts of ill-conditioned data typical of modern manufacturing environments[1].Although the PLS algorithm is known to handle mild non-linearities present in the data, it is also well accepted that these non-linearities can be more intense and hence the PLS method will not fit the data properly. Quadratic Non-linear forms of the PLS method have been proposed[2,3] to address these limitations of the PLS method as well as many other proposals using a hybrid approach of PLS with neural networks[4]

This work presents an augmentation to the non-linear version of the PLS method presented by Wold and Hosskuldsson solving internal steps of the NIPALS algorithm using non-linear programming methods. The aim of this work is to provide a ?generic? non-linear form of the PLS algorithm by using a robust parameter estimation approach that enables the proposal of any non-linear function between the t and the u scores. The method is illustrated with examples from the pharmaceutical sector.

Although an improvement over the previous algorithm, the authors still consider this approach a sub-optimal solution to the problem and are currently working on an improved approach where the complete parameter estimation problem is solved in one formulation instead of using iterative approaches to the problem.

Literature Cited

(1) MacGregor, J. F.; Yu, H.; Garcia-Munoz, S.; and Flores-Cerrillo, J. Data-based latent variable methods for process analysis monitoring and control. Comput.Chem.Engng. 2005, 29, 1217-1223. (2) Hoskuldsson, A. Quadratic PLS Regression. J.Chemometrics 1992, 6, 307-334. (3) Wold, S.; Kettaneh, N.; and Skagerbergt, B. Nonlinear PLS Modeling. Chemom.Intell.Lab.Syst. 1989, 7, 53-65. (4) Qin, S. J. ; McAvoy, T. J. Nonlinear PLS modeling using neural networks. Computers & Chemical Engineering 1992, 16 (4), 379-391.