A Generalized Multivariate Method for Quantification in Gray Systems

Analyte determination in the presence of unexpected sample constituents, i.e., those not taken into account in the calibration phase, is one of the important subjects in the field of chemometrics. Multivariate calibration methods are a group of techniques based on factor analysis with the goal to develop the mathematical models relating unselective multiple instrumental signals with analyte concentrations. The area of calibration can be divided in zero, first and second-order, etc. A given instrument may yield first-order (vector) data for a single sample, which, when several samples are combined into a matrix, produces a two-way array. Principal component regression (PCR) and Partial Least Square (PLS) are two well-established algorithms in first-order multivariate calibrations which allow the simultaneous determination of multiple analytes in the same sample. In first-order calibration methods, calibration samples must contain the same potential interferents as unknown samples [1]. Several modified first order calibration methods tried to quantify analytes in the presence of unexpected constituents (in gray samples). Unfortunately all of those methods can only give a possible solution because of lack of information needed for unique solution [2]. In this work the main aim is introduction of a general method to calculate all of the possible solution in a very simple way. In addition, all information that must be added to these systems to cause uniqueness has been discussed. Based on duality relation it is obvious that any information about the spectra of interferents could be useful in the accuracy of analyte quantification. Now the question is what is the least information that would be useful in accuracy of quantification? In the last step, a graphical user-friendly interface (GUI) has been designed to make the program easier to use. Simulated data sets and real systems have been used to evaluate the performance of proposed method. In this work quercetin as an antioxidant has been determined in honey and onion as real samples.