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 square-summed 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.