Newer developments on self-modeling curve resolution implementing equality and unimodality constraints

Definition and detection of data-based uniqueness in evaluating bilinear (two-way) chemical measurements

“…Eq. (3) shows the normalized matrix T and its inverse T À1 : [26]. This event can also happen when two interferences are determined uniquely.…”

“…Three sections surrounded by Borgen triangles specify three permitted areas that contain feasible regions. In most data sets, the permitted areas are not identical with the feasible regions, and it is considered an exceptional case when there is at least one unique solution in one mode [26]. Because of the unique solution for at least one component in this latter case, Borgen triangles are enough to compute the feasible region since the simplex rotation is limited to Borgen triangles due to the intersection point between inner and outer polygons [26].…”

“…This phenomenon is the so-called partial uniqueness [31] that refers to systems in which one factor is recovered uniquely. (2) Because of the unique resolution of the first component profiles, the potential locations of the feasible solutions are restricted to line segments for the complementary components and simplified, exactly, to Lawton-Sylvestre (LS) plot [26].…”

Fitting-free curve resolution of spectroscopic data: Chemometric and physical chemical viewpoints

“…should be avoided, because it can cause harmful artefact results [37]. Interestingly, the problem in this paper is related to spectral equality constraint [24] using for all components. However, we assume that the spectra can be used to generate the data set, though due to real measurement, bilinearity can be slightly corrupted, because of the band shifting of spectra.…”

“…Another example for curve resolution method is independent component analysis (ICA) [21,22]. ICA and other curve resolution methods [23] suffer from the rotational ambiguity [24,25] of the bilinear data. It means that these procedures can provide only one solution, but it may be not unique.…”