Calibration transfer as a data reconstruction problem

Abstract

Another approach to calibration transfer has been developed based on a relatively new factorization technique, positive matrix factorization (PMF). PMF was developed and initially applied to environment data analysis. It has important differences from principal component analysis (PCA). Since it is a least squares approach to solving the factor analysis problem, it can use subjective weights for individual data points and thereby make it possible to include uncertain data points like missing or below detection limit values in the analysis. Because of PMF's ability to handle missing data, the problem of calibration transfer among instruments or experimental conditions is posed as a missing data problem in which the spectra on a secondary instrument (or alternative experimental condition) are missing. PMF analysis is applied to a data matrix of known calibration sample spectra from the primary instrument, a subset of the standardization samples measured on both the primary and secondary instruments, the measured spectra of prediction samples on the secondary instrument and the unknown spectra (missing values) of the prediction samples on the primary instrument. From the factors derived from these data, the missing values of the spectra of prediction samples on the primary instrument are estimated. The spectra of the prediction samples are thereby transferred from the secondary instrument to the primary one where the calibration model was built. Calibration models built on the primary instrument are applied to the transferred spectra and concentrations of prediction samples are thus estimated. The proposed method has been tested by both simulated and measured NIR data sets.