Recent developments of chemical multiway calibration methodologies with second‐order or higher‐order advantages

Abstract

Developments in chemical multiway calibration methodologies in chemometrics that have taken place in tune with advances in modern (hyphenated) analytical instrumentation have been reviewed in this article. These advances in the ability to predict the concentration of an analyte using information‐rich data collected from such instruments are outstanding examples of the philosophy of analytical method development outlined by Bruce R. Kowalski more than three decades ago. With the increase in the complexity of analytical objects, sophistication in analytical instrumentation has also been enhanced. Chemometrics classifies analytical instruments as zeroth‐order, first‐order, second‐order, and higher‐order according to the order of data that the instrument produces. Different multiway calibration methodologies have been developed to calibrate the instrument and predict the concentration of analytes. In this review, select works of Kowalski and co‐workers in the context of second‐order calibrations, as well as other recent developments in multiway calibration, especially the three‐way and four‐way calibrations, which preserve the second‐order or high‐order advantages, are highlighted. Copyright © 2013 John Wiley & Sons, Ltd.

Chemical rank estimation for second-order calibration by discrete Fourier transform coupled with robust statistical analysis

“…The singular values obtained by performing SVD on the total matrix were plotted in decreasing order ( Figure 2D). The contour and three-dimensional plots shown A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 13 in Figure 2C imply that the signal-to-noise ratio of the dataset was relatively low. The result shows that only two significant components were present in the analytical system.…”

“…In this kind of analysis, the accurate number of components in a dataset necessary to provide valuable resolutions is difficult to determine [1][2][3][4][5]. To date, methods for overlapped signal resolution have been extensively studied, and chemometric methodologies that include multivariate curve resolution [6][7][8][9][10] and second-order calibration [11][12][13] have been widely accepted in various reports. Significant advantages of these methods include separation of overlapped chemical signals using a mathematical separation strategy and accurate quantification of analytes.…”

Solving signal instability to maintain the second-order advantage in the resolution and determination of multi-analytes in complex systems by modeling liquid chromatography–mass spectrometry data using alternating trilinear decomposition method assisted with piecewise direct standardization

“…Therefore, ATLD method became the best candidate to analyze the three-way large-scale LC-MS experimental data. More detailed information for ATLD method can be found in the previously published references [44,[54][55][56][57].…”

Unfolded and Multiway Partial Least-Squares with Residual Multilinearization

“…They would display the obvious advantage of providing richer analytical information, implying more stable methods toward interferences and matrix effects, and less prone to minor changes in reaction conditions, which should allow for an improvement in predictive ability. In addition, improvements in sensitivity and the resolution of collinearity problems have been reported [38]. However, it is a fact that only few experimental four-way data have been recorded and used to develop analytical methodologies to date, which can be attributed to the fact that the practical acquisition of these data arrays is still difficult to implement.…”