On the signal contribution function with respect to different norms

Abstract

The signal contribution function (SCF) in multivariate curve resolution evaluates signal portions of specific components either in absolute or in relative form related to the integrated signal of all components. In 1999, Gemperline used the summed signal data, and in 2001, Tauler worked with the squaresummed relative signal in order to determine the profiles that minimize, respectively maximize, the signal contribution. These profiles approximate the bands of all feasible profiles. Here, Gemperline's approach using the entrywise 1-matrix norm is proved to provide accurate bounds for two-component systems. This revives the approach of summed mass or absorption values with its potentially better chemical interpretability.

Two new methods for the estimation and interpretation of the range of feasible profiles in multivariate curve resolution and their implications to analytical chemistry

“…The green circle and red cross corresponding to maximum profiles match, in contrast to the green square and the red asterisk for the minimum ones. Incidentally, Figure 6B also shows that the projections of the extreme profiles are located in the border of the corresponding AFS, as expected 24,28 …”

“…Incidentally, Figure 6B also shows that the projections of the extreme profiles are located in the border of the corresponding AFS, as expected. 24,28 Regarding the simulated system S2, it involves the same spectra as in system S1, but the time profiles are augmented with the purpose of mimicking a real calibration scenario, as described above. In this case an additional constraint can be applied, i.e., the correspondence between species and samples.…”