Multi-way chemometric methodologies and applications: A central summary of our research work

A novel fourth-order calibration method based on alternating quinquelinear decomposition algorithm for processing high performance liquid chromatography–diode array detection– kinetic-pH data of naptalam hydrolysis

“…These algorithms hold the second-order advantage which is known as the ability to accurately achieve the concentrations of individual component of interest through separating the signals of target analyte(s) from those of uncalibrated background or interferences. They have been applied in many scientific fields, such as chemistry, medicine, food, environmental and single-cell science, as can be seen from an explosion in the volume of relevant literatures [7][8][9][10][11].…”

Second-order advantage obtained from standard addition first-order instrumental data and multivariate curve resolution-alternating least squares. Calculation of the feasible bands of results

“…One data mode refers to the compositional variation of the system and the other ones are related to the variation in the collected responses in the instrumental modes. When the number of data modes increases, different data-processing and mathematical algorithms are required for the convenient study of this body of information [1]. A calibration model obtained from multi-way measurements allows one not only to mark new samples containing components which do not take part in the calibration data set, but also to quantitate the analyte of interest without knowledge of the interfering chemical components that may be present in complex chemical matrices [2][3][4][5][6][7], a property known as the second-order advantage [8].…”

Four-way Self-weighted Alternating Normalized Residue Fitting Algorithm with Application for the Analysis of Serotonin in Human Plasma

“…The inner cyclic symmetry property exits in multilinear decomposition. 15 The four-way cyclic symmetry of quadriclinear decomposition, which is a feature of four-way data, is an extension of the cyclic symmetry of trilinear decomposition. As visualized in Fig.…”

“…[1][2][3] Nowadays, "second-order calibration" should be considered as the most popular multi-way data analysis method; this includes, for instance, the generalized rank annihilation method (GRAM), [4][5][6] parallel factor analysis (PARAFAC), [7][8][9][10] alternating trilinear decomposition (ATLD), 11 self-weighted alternating normalized residue fitting (SWANRF) 12 and so on. [13][14][15][16][17][18] They aim to search for any "second-order advantage" by three-dimensional responsive data; that is, second-order calibration has better stability towards interferents as well as matrix effects. Thus, they have been brought into extensive practical applications, for example, biological matrices, pharmaceuticals, food, and environment, [19][20][21][22][23][24][25][26][27] while seeking out a way to quantify the analytes of interest, even in presence of complex background.…”