Calibration transfer as a data reconstruction problem

Another approach to calibration transfer has been developed based on a rela tively new factorization technique, positive matrix factorization (PMF). PM F 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 val ues in the analysis. Because of PMF's ability to handle missing data, the p roblem of calibration transfer among instruments or experimental conditions is posed as a missing data problem in which the spectra on a secondary ins trument (or alternative experimental condition) are missing. PMF analysis i s applied to a data matrix of known calibration sample spectra from the pri mary instrument, a subset of the standardization samples measured on both t he primary and secondary instruments, the measured spectra of prediction sa mples on the secondary instrument and the unknown spectra (missing values) of the prediction samples on the primary instrument. From the factors deriv ed from these data, the missing values of the spectra of prediction samples on the primary instrument are estimated. The spectra of the prediction sam ples are thereby transferred from the secondary instrument to the primary o ne where the calibration model was built. Calibration models built on the p rimary instrument are applied to the transferred spectra and concentrations of prediction samples are thus estimated. The proposed method has been tes ted by both simulated and measured NIR data sets. (C) 1999 Elsevier Science B.V. All rights reserved.