Recent advances in analytical calibration with multi-way data

Analytical Figures of Merit: From Univariate to Multiway Calibration

“…20 By processing these data, considerably more complex analytical problems can be solved, [21][22][23][24][25][26][27][28][29][30][31] and predictions are even possible in the presence of unexpected spectral interferences, i.e., sample constituents not considered in the calibration phase. 32 The latter will be called, in the remainder of this paper, simply as 'unexpected interferences'.…”

“…32 Interesting experimental applications in which this advantage has been exploited for a variety of samples can be found in recent reviews. [22][23][24][25][26][27][28][29][30][31] An alternative nomenclature is based on the number of ways, which is equivalent to the number of modes of a data array for a group of samples. 32 Thus univariate and one-way calibration are synonymous, as are first-order and two-way calibration, second-order and threeway calibration, etc.…”

“…Details on the operation of all these algorithms can be found in the Supporting Information and in relevant reviews. [22][23][24][25][26] At the risk of some oversimplification, Table 1 shows a correspondence between data properties and algorithms. Multi-linear algorithms such as PARAFAC are the natural choice for multi-linear data, extended MCR-ALS is based on an augmented bilinear matrix and hence it is also natural to select it when the data are non-multi-linear but follows the augmented bilinear model, and finally latent-variable PLS/RML methodologies display a flexibility which should made them the algorithms of choice for other non-multilinear data.…”

“…[21][22][23][24][25][26]109 The sensitivity increase can now be precisely computed using the general expression (18). This may …”

Unfolded and Multiway Partial Least-Squares with Residual Multilinearization

“…Regrettably, the increased flexibility comes at the price of some disadvantages; the most conspicuous one is the inability of U-PLS/RBL and N-PLS/RBL to render approximations to pure constituent profiles, thereby loosing chemical interpretability for the sake of accurate analyte quantitation. It is interesting that U-PLS/RBL and N-PLS/RBL were developed in 1990 [7], later abandoned and recently rediscovered [8], and successfully applied to a variety of analytical systems [9,10].…”