Alternating penalty trilinear decomposition algorithm for second‐order calibration with application to interference‐free analysis of excitation–emission matrix fluorescence data

Abstract

A new method, alternating penalty trilinear decomposition (APTLD), is developed for the decomposition of three-way data arrays. By utilizing the alternating least squares principle and alternating penalty constraints to minimize three different alternating penalty errors simultaneously, the intrinsic profiles are found. The APTLD algorithm can avoid the two-factor degeneracy problem and relieve the slow convergence problem, which is difficult to handle for the traditional parallel factor analysis (PARAFAC) algorithm. It retains the second-order advantage of quantification for analytes of interest even in the presence of potentially unknown interferents. In additions, it is insensitive to the estimated component number, thus avoiding the difficulty of determining a correct component number for the model, which is intrinsic in the PARAFAC algorithm. The results of treating one simulated and one real excitation-emission spectral data set showed that the proposed algorithm performs well as long as the model dimensionality chosen is not less than the actual number of components. Furthermore, the performance of the APTLD algorithm sometimes surpasses that of the PARAFAC algorithm in the prediction of concentration profiles even if the component number chosen is the same as the actual number of underlying factors in real samples.

Second- and higher-order data generation and calibration: A tutorial

“…Additional algorithms based on trilinear modelling of three-way arrays are self-230 weighted alternating trilinear decomposition (SWATLD) [20] and penalized alternating 231 trilinear decomposition (APTLD) [21]. Other less employed algorithms in this context 232 are generalized rank annihilation (GRAM) [22], direct trilinear decomposition (DTLD) 233 [23] and bilinear least-squares (BLLS) [24], either because the use single calibration 234…”

Chemometric strategies for enhancing the chromatographic methodologies with second-order data analysis of compounds when peaks are overlapped

“…Comprehensive information about the different second-order algorithms can be found in the pertinent literature [13][14][15][16][17][18][19][20][21]. In addition, complete reviews were presented with a wide range of applications to second-order data (including chromatography) [6][7][8].…”

“…generalized rank annihilation (GRAM) [13], direct trilinear decomposition (DTLD) [14,15], selfweighted alternating trilinear decomposition (SWATLD) [16], alternating penalty trilinear decomposition (APTLD) [17], parallel factor analysis (PARAFAC) [18], multivariate curve resolution alternating least squares (MCR-ALS) [19], and the most recently implemented bilinear least squares (BLLS) [20], unfolded partial least squares/residual bilinearization (U-PLS/RBL) [21] and artificial neural networks followed by residual bilinearization (ANN/RBL) [22].…”

Rank annihilation factor analysis for multicomponent kinetic‐spectrophotometric determination using difference spectra

“…Bilinear data sets can be linked and the global analysis of the complete set can be a significant advantage [2]. Suitable algorithms for analyzing second-order data are parallel factor analysis (PARAFAC) [3], the generalized rank annihilation method (GRAM) [4], direct trilinear decomposition (DTLD) [5], multivariate curve resolution-alternating least squares (MCR-ALS) [6], bilinear least squares (BLLS) [7,8], alternating trilinear decomposition (ATLD) [9] and its variants (self-weighted alternating trilinear decomposition (SWATLD) [10] and alternating penalty trilinear decomposition (APTLD) [11,12]). These algorithms are of prime relevance to the analysis of complex mixtures, because they poses the second-order advantage.…”