Updating Multivariate Calibrations with the Delaunay Triangulation Method

Multivariate calibrations must be updated when new samples show different spectral characteristics. In this paper, we discuss how to do this when the calibration is performed with a topological multivariate calibration method based on Delaunay triangulation (DT). The updating leads either to the expansion of the original calibration set or to the creation of a new local model. Outliers in the new samples with respect to the original calibration set are first detected and divided in two groups, namely, marginal outliers, which are considered to be extensions of the calibration set and are used for updating the calibration set, and true outliers. If a sufficient number of true outliers are found to be situated close enough to each other, they can form the basis for a new local model. Several updating simulations performed on a real data set show that the updating procedure performs well. The results for prediction with the DT method after updating are comparable to or better than those after updating with partial least squares (PLS) and it is concluded that, in many cases, the DT method is a valuable alternative for multivariate calibration.