Calibration methods for spectral chemical data.

Abstract

Quantitative analyses involving instrumental signals, such as chromatograms, NIR, and MIR spectra have been successfully applied nowadays for the solution of important chemical tasks. Multivariate calibration is very useful for such purposes, but as the number of descriptors increases, regression models can become problematic in many cases. A problem likely to occur in large descriptor sets, for example, is information redundancy when descriptors are substantially correlated with each other. Latent variable methods have become accepted methods of addressing this issue. These methods are Principal Component Regression (PCR) and Partial Least Squares (PLS) regression. PLS is one of the most commonly used multivariate calibration methods: it deals with so-called ill-posed problems often produced as a consequence of strong correlation between the measured variables or large number of measurements in comparison with the number of recorded samples. However, using PLS, nonlinear relations can be modeled in a limited way as taking into account more latent variables. Introducing regression methods based on Support Vector Machines method (SVM) in chemometrics presents alternatives to the existing linear and non-linear multivariate calibration approaches. SVM has the advantage that it can treat both linear and non-linear data sets, so the trouble of under fitting can be controlled or reduced in some problems. SVM-based regressions are able to solve ill-posed problems leading to models that are often unique and exhibit good prediction power. Some results obtained using of a variant of support vector based method (relevance vector machine) as a multivariate calibration method is presented. The commonly used methods in chemometrics consider each sample spectrum as a sequence of discrete data points. An alternative way to analyze spectral data is to consider each sample as a function, in which a functional data is obtained. The use of support vector regression for functional data (FDA-SVR) for the solution of linear and nonlinear multivariate calibration problems is presented. Three different spectral datasets were analyzed and a comparative study was carried out to test its performance with respect to some traditional calibration methods used in chemometrics such as PLS, SVR and LS-SVR. Keyword: multivariate calibration, regression, support vector regression, functional data analysis