Abstract
In many areas of research and industrial situations, including many data analytic problems in chemistry, a strong nonlinear relation
between different sets of data may exist. While linear models may be a good simple approximation to these problems, when nonlinearity is
severe they often perform unacceptably. The nonlinear partial least squares (PLS) method was developed in the area
of chemical data analysis. A specific feature of PLS is that relations between sets of observed variables are modeled by means of latent
variables usually not directly observed and measured. Since its introduction, two methodologically different concepts of fitting existing
nonlinear relationships initiated development of a series of different nonlinear PLS models. General principles of the two concepts and
representative models are reviewed in this chapter. The aim of the chapter is two-fold i) to clearly summarize achieved results and
thus ii) to motivate development of new computationally efficient nonlinear PLS models with better performance and good interpretability.
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