Graphical representation of two-dimensional correlation in vector space

Abstract

The concept of two-dimensional (2D) correlation analysis may be regarded as a form of manipulation and comparison of vectors, representing spectral intensity variations measured at two independent spectral variables along a perturbation variable. Such vector operations can be represented graphically for easier visualization. Graphical representation provides a more intuitive understanding of different forms of 2D correlation methods. Interestingly, we observed that synchronous correlation and disrelation analysis seem to form a more natural pair as complementary techniques, because they share very similar sets of vector manipulations, although some steps of operations are geometrically perpendicular to each other. Asynchronous correlation, on the other hand, seems to belong to a different class of vector operations, as it is not confined to a fixed plane in a vector space but spans additional dimensions. This finding suggests the possible existence of many other vector comparison methods not yet being explored by utilizing the full scope of a given vector space. The graphical representation not only gives a unified tool to compare various forms of current 2D correlation methods but also may potentially assist further evolution of useful correlation methods not yet being developed.