Analysis of variation matrix array by bilinear least squares–residual bilinearization (BLLS–RBL) for resolving and quantifying of foodstuff dyes in a candy sample

• Analysis pH-spectrophotometric three-way data by using variation matrix.
• Application of variation matrix in bilinear least square-residual bilinearization.
• Simultaneous determination Sunset yellow and Carmosine in the presence of unknown interference.

Bilinear least square (BLLS) method is one of the most suitable algorithms for second-order calibration. Original BLLS method is not applicable to the second order pH-spectral data when an analyte has more than one spectroscopically active species. Bilinear least square-residual bilinearization (BLLS–RBL) was developed to achieve the second order advantage for analysis of complex mixtures. Although the modified method is useful, the pure profiles cannot be obtained and only the linear combination will be obtained. Moreover, for prediction of analyte in an unknown sample, the original algorithm of RBL may diverge; instead of converging to the desired analyte concentrations. Therefore, Gauss Newton-RLB algorithm should be used, which is not as simple as original protocol. Also, the analyte concentration can be predicted on the basis of each of the equilibrating species of the component of interest that are not exactly the same.The aim of the present work is to tackle the non-uniqueness problem in the second order calibration of monoprotic acid mixtures and divergence of RBL. Each pH-absorbance matrix was pretreated by subtraction of the first spectrum from other spectra in the data set to produce full rank array that is called variation matrix. Then variation matrices were analyzed uniquely by original BLLS–RBL that is more parsimonious than its modified counterpart. The proposed method was performed on the simulated as well as the analysis of real data. Sunset yellow and Carmosine as monoprotic acids were determined in candy sample in the presence of unknown interference by this method.

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