On the least size of first-order calibration model using multivariate curve resolution methods

Several analytical applications of multivariate calibration methods require decision about the number of samples used for building the regression model. Calibration set should ideally be large enough and representative to produce reliable prediction [1]. In practice, however, the large number of calibration samples is costly in terms of time and effort. Some studies have been done to develop advanced regression techniques that are able to provide robust models from a limited number of calibration samples. In this work, a general rule for finding the minimum number of samples that must be acquired in a calibration problem is presented. The theoretical proofs, demonstrated both algebraically and geometrically, are based on the required number of known values for calculating the concentration profile of an analyte in a multicomponent system. The Partial least squares (PLS) [2], that often is referred to as a standard first order calibration, and also the correlation constraint multivariate curve resolution (CCMCR) [3] were used to assess the presented rules in several case studies.