Novel constrained PARAFAC algorithm for second-order linear calibration Original Research Article

A novel constrained PARAFAC was designed to mitigate the influence of model deviations on the predictive accuracy in second-order calibration. It combines the two steps of decomposition and calibration of PARAFAC in second-order calibration into just one step by imposing the concentrations of the calibration samples on the model parameters in the third mode as constraints. Such a scheme not only simplifies the whole calibration procedure, but also renders some extra advantages over PARAFAC when model deviations such as Rayleigh scattering in fluorescence spectroscopy present in measurements. The results for fluorescent and HPLC data arrays have demonstrated that the relative deviations of the predicted concentrations could be significantly reduced when the constrained version of PARAFAC replaces PARAFAC to do second-order linear calibration.