Comparison of Principal Component Analysis and Generalized Two-Dimensional Correlation Spectroscopy: Spectral Analysis of Synthetic Model System and Near-Infrared Spectra of Milk

Abstract

Principal component analysis (PCA) and generalized two-dimensional (2D) correlation spectroscopy have been applied to a two-component spectral model made up of highly overlapped bands and to near-infrared (NIR) spectra of milk. The analyses were made on mean-normalized and mean-centered data of the model. The dynamic loading of PCA is expanded into 2D contour by calculating a variance-covariance matrix. This 2D pattern is compared with a synchronous 2D spectrum calculated by generalized 2D correlation spectroscopy, and a high degree of similarity is discernible between the two kinds of 2D spectra. The one-dimensional (1D) features of the synchronous 2D map, slice spectra, are identical to the dynamic loading as well. We show that, for noncentered data of the model system, only in limited cases can the correlation between the first loadings and synchronous map be established. PCA of the milk spectra yields two factors. The 2D representation of the most important loading is significantly different from the synchronous spectrum calculated by the generalized 2D approach. The slice spectra from which the synchronous spectrum is made are found to be mutually different as one moves along the variable axis. A synchronous 2D map emphasizes only variables with the highest correlation of the spectral intensity changes. On the other hand, PCA is geometrically oriented; thus, as the complexity of the data increases, the differences between PCA and generalized 2D correlation spectroscopy become striking. The selectivity of the asynchronous 2D map is demonstrated for the bands due to milk fat.