Multivariate Calibration with the Delaunay Triangulation Method: Definition of the Calibration Domain

The Delaunay triangulation (DT) method for multivariate calibration is a topological multivariate calibration method. In this paper, we present methods for the definition of the calibration domain. Outliers in the calibration set must be found and deleted and clusters detected. When clusters are found, it may be advantageous to make separate local models. Two methods are proposed. The first, called the DT calibration domain algorithm, is based on finding a kernel of samples that is then extended according to local rules. An alternative is to first eliminate gross outliers and then divide the data set in clusters, if such clusters exist, with Dbscan, a density‐based clustering method. The cluster(s) is (are) then used as kernels(s) and extended with the same rules as the DT calibration domain algorithm to develop DT models for each cluster. The two methods and some of the difficulties that can be encountered with them are demonstrated with three simulated data sets and tested with three real NIR data sets (one agricultural, one food, and one industrial). It is shown that the methods perform well and are at least comparable in prediction performance to partial least squares (PLS).