Nonlinear partial least squares

Wold, H. Chemom. Intell. Lab. Syst. 14, 1992, 71-84. Nonlinear partial least squares modelling II. Spline inner relation. 

Hasegawa, K., Kimura, T., Miyashita, Y. and Funatsu, K. (1996a). Nonlinear Partial Least Squares Modeling of Phenyl Alkylamines with the Monoamine Qxidase Inhibitory Activities. J.Chem.Inf.Comput.Sci.,36,1025-1029. 

EC Malthouse, AC Tamhane, and RSH Mah. Nonlinear partial least squares. Comput. Chem. Engg., 21(8) 875-890, 1997. 

Kimura, T., Miyashita, Y, Eunatsu, K. and Sasaki, S.l. (1996) Quantitative structure-activity relationships of the synthetic substrates for elastase enzyme using nonlinear partial least squares regression. J. Chem. Inf. Comput. Sci., 36, 185—189. 

In this section, on the one hand, methods that are used to estimate intrinsically nonlinear parameters by means of nonlinear regression (NLR) analysis will be introduced. On the other hand, we will learn about methods that are based on nonpara-metric, nonlinear modeling. Among those are nonlinear partial least squares (NPLS), the method of alternating conditional expectations (ACE), and multivariate adaptive regression splines (MARS). 

F Doymaz, A Palazoglu, and JA Romagnoli. Orthogonal nonlinear partial least-squares. Ind. Eng. Chem. Research, 42 5836-5849, 2003. 

An older general review by Stefan et al. [2] considers mathematical modeling for data processing (including a variety of chemometric methods such as linear and nonlinear partial least squares, fuzzy neural networks, and multivariate analysis of variance), designs for electrochemical sensor arrays as well as applications in environmental, food and clinical analysis. Arrays of potentiometric ion-selective electrodes, piezoelectric crystal sensors, and voltammetric biosensors, as well as the electronic nose gas-phase sensor arrays are reviewed. 

The nonlinear iterative partial least-squares (NIPALS) algorithm, also called power method, has been popular especially in the early time of PCA applications in chemistry an extended version is used in PLS regression. The algorithm is efficient if only a few PCA components are required because the components are calculated step-by-step. 

NIPALS Nonlinear iterative partial least-squares... 

Wold, H. Soft Modeling by Latent Variables the Nonlinear Iterative Partial Least Squares Approach," Ed. J. Gani, in Perspective in Probability and Statistics - Papers in Honor of M. S. Bartlett, Academic Press, London 1975, pp. 117-142... 

D.K. Melgaard and D.M. Haaland, Comparisons of prediction abilities of augmented classical least squares and partial least squares with realistic simulated data effects of uncorrelated and correlated errors with nonlinearities, Appl. Spectrosc., 58, 1065-73 (2004). 

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