Multivariate Calibration with Least-Squares Support Vector Machines

This paper proposes the use of least-squares support vector machines (LS-SVMs) as a relatively new nonlinear multivariate calibration method, capable of dealing with ill-posed problems. LS-SVMs are an extension of “traditional” SVMs that have been introduced recently in the field of chemistry and chemometrics. The advantages of SVM-based methods over many other methods are that these lead to global models that are often unique, and nonlinear regression can be performed easily as an extension to linear regression. An additional advantage of LS-SVM (compared to SVM) is that model calculation and optimization can be performed relatively fast. As a test case to study the use of LS-SVM, the well-known and important chemical problem is considered in which spectra are affected by nonlinear interferences. As one specific example, a commonly used case is studied in which near-infrared spectra are affected by temperature-induced spectral variation. Using this test case, model optimization, pruning, and model interpretation of the LS-SVM have been demonstrated. Furthermore, excellent performance of the LS-SVM, compared to other approaches, has been presented on the specific example. Therefore, it can be concluded that LS-SVMs can be seen as very promising techniques to solve ill-posed problems. Furthermore, these have been shown to lead to robust models in cases of spectral variations due to nonlinear interferences.