Derivation of the generalized rank annihilation method (GRAM)
نویسنده
چکیده
Introduction The generalized rank annihilation method (GRAM) is a method for curve resolution and calibration that requires only a single calibration sample to obtain the socalled second-order advantage, i.e., it can determine the analyte of interest in the presence of unsuspected interferences [1]. GRAM is only one of many competing methods that can be applied to this particular data set-up. However, GRAM stands out for two reasons. First, its error analysis is extensively studied, see e.g. [2,3]. Second, GRAM has been reported to compare favorably with alternating least squares (ALS), alternating trilinear decomposition (ATLD), alternating coupled vectors resolution (ACOVER), alternating slice-wise diagonalization (ASD), alternating coupled matrices resolution (ACOMAR), self-weighted alternating trilinear decomposition (SWATLD) and pseudo alternating least squares (PALS), see [4]. Currently, no useful generalization of GRAM to multiple calibration samples seems to exist [5], however. Several derivations of GRAM are published in the chemometrics literature, but they tend to be complicated. The remainder of this note consists of (1) a derivation that requires fewer steps and (2) a discussion that intends to shed some light on the properties of the solution.
منابع مشابه
Simultaneous spectrofluorometric determination of piroxicam and pyridoxine using generalized rank annihilation method.
The application of generalized rank annihilation method (GRAM) to the analysis of fluorescence excitation-emission matrices of mixtures of piroxicam and pyridoxine is described. The input of GRAM consists of two bilinear data matrices, i.e. one for unknown and one for the calibration sample. The excitation wavelength range was from 290 to 340 nm and the emission was recorded from 370 to 560 nm....
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