A combined artificial neural network/residual bilinearization approach for obtaining the second‐order advantage from three‐way non‐linear data

Abstract

Three-way instrumental data offer the second-order advantage to analysts, a property of great utility in the field of complex sample analysis in the presence of unsuspected components as potential interferents. The available multivariate methodologies for obtaining this advantage are all based on linear models, and hence they are not applicable to spectral information behaving in a non-linear manner with respect to target analyte concentrations. This work describes the combination of a backpropagation artificial neural network model with a technique known as residual bilinearization, applicable to second-order spectral information. The joint model allows one to efficiently extract analyte concentrations from intrinsically non-linear data, even in the presence of unsuspected constituents. Simulations have been performed by mimicking deviations from linearity brought about by: (1) exponential relationship between fluorescence and concentration, (2) kinetic evolution of responsive reaction products and (3) analytes acting as reaction catalysts. In all of these cases, successful prediction of the analyte concentrations was achieved on large test sample sets, which included the presence of overlapping components not included in the training step. The new method not only obtains the second-order advantage, but also correctly retrieves the contribution of the unsuspected components to the total test sample signals. The comparison with a multivariate methodology based on partial least-squares regression with second-order advantage shows that the presently described method displays better predictive ability.

Partial Least-Squares with Residual Bilinearization

“…19 The purpose of this latter algorithm is to process three-way/ second-order calibration data where significant nonlinearities exist in the signal-concentration relationship. 22 The description of these nonlinear three-way/secondorder calibration methods is beyond the scope of this book; the reader may find interesting discussions and applications in some relevant references. matrix obtained by placing the unfolded vectors adjacent to each other, in the same manner as that described for U-PLS calibration.…”

MATLAB in electrochemistry: A review

“…[22,23]. The second group of methods, based on residual bilinearization, comprise: 1) bilinear least-squares followed by RBL (BLLS/RBL) [24,25], 2) unfolded partial least-squares/RBL (U-PLS/RBL) [26,27], 3) multidimensional partial least-squares/RBL (N-PLS/RBL) [28,29], and unfolded principal component analysis/RBL (U-PCA/RBL) [30]. The latter methodology has been devised in order to produce suitably preprocessed data from non-linear instrumental data, for further analysis using artificial neural networks [31,32].…”

Validation and Error

“…52 More complex, that is, four-way data, where each sample produces a third-order tensor, such as, for example, time evolving EEMs, have been recently described and applied to obtain the second-order advantage. A recent proposal, for example, involves coupling artificial neural networks with posttraining RBL to achieve the second-order advantage from second-order instrumental data.…”