A retrospective view on non-linear methods in chemometrics, and future directions

Abstract

This perspective article reviews how the chemometrics community approached non-linear methods in the early years. In addition to the basic chemometric methods, some methods that fall under the term “machine learning” are also mentioned. Thereafter, types of non-linearity are briefly presented, followed by discussions on important aspects of modeling related to non-linear data. Lastly, a simulated data set with non-linear properties is analyzed for quantitative prediction and batch monitoring. The conclusion is that the latent variable methods to a large extent handle non-linearities by adding more linear combinations of the original variables. Nevertheless, with strong non-linearities between the X and Y space, non-linear methods such as Support Vector Machines might improve prediction performance at the cost of interpretability into both the sample and variable space. Applying multiple local models can improve performance compared to a single global model, of both linear and non-linear nature. When non-linear methods are applied, the need for conservative model validation is even more important. Another approach is pre-processing of the data which can make the data more linear before the actual modeling and prediction phase.