New Approach to Generalized Two-Dimensional Correlation Spectroscopy. IV: Eigenvalue Manipulation Transformation (EMT) for Partial Attenuation of Dominant Factors

Abstract

This paper extends our previous work on the potential of eigenvalue manipulating transformation (EMT) of a data matrix for spectral selectivity enhancement in two-dimensional (2D) correlation analysis. EMT operation by uniformly lowering the power of a set of eigenvalues associated with the original data exaggerates the information content of minor principal components and reduces that of major principal components. Thus, much more subtle differences of spectral behavior for each component are now highlighted. Similarly, the selective truncation of dominant principal component (PC) factors to bring up the subtle contributions of minor factors is also considered. The EMT-reconstructed data matrix where power parameter m is negative greatly reduces the contribution of the first PC. Hybrid models for the attenuation of the contribution of the first PC are discussed. Synchronous 2D correlation spectra from PC1-attenuated data matrix A** obtained by varying the value of the attenuation parameter k show a much more profound effect than asynchronous 2D correlation spectra. As the value of k is increased, features of 2D correlation spectra start looking very much like those from the principle component analysis (PCA)-reconstructed data with only the second and third PCs and from the EMT-reconstructed data matrix where the power parameter m is negative.