Statistical two-dimensional correlation spectroscopy: its theory and applications to sets of vibrational spectra

The present study aims at developing a new form of two-dimensional (2D) correlation spectroscopy, statistical 2D correlation spectroscopy. Statistical 2D spectroscopy differs from the widely used generalized 2D correlation spectroscopy in that the former abstracts spectral features by pretreatment and by 2D maps that are limited by the correlation coefficients in the range from 1 to -1. In this paper, the theory of the new 2D method is briefly described, and then its applications are discussed to reveal spectral and concentration features of artificial model spectra, infrared spectra of polycondensation of bis(hydroxyethyl terephthalate) measured on-line, and short-wave near-infrared spectra of raw milk. The results are analyzed thoroughly and compared with those from generalized 2D correlation spectroscopy and partial least-squares loadings and scores. The most significant advantage of statistical 2D correlation spectroscopy is that the 2D correlation spectra are easy to calculate and are purely mathematical in nature, thereby eliminating any subjective involvement of an experimenter, while the inherent weakness of the method lies in its sensitivity to the noise.