Two-dimensional correlation analysis

This tutorial reviews the recent computational advances in two-dimensional (2D) correlation spectroscopy, presents the theory, and provides examples applying 2D correlation analysis. Two-dimensional correlation analysis is a method for visualizing the relationships among the variables in multivariate data and their temporal behavior by applying the complex cross-correlation function. This function measures correlations that occur at the same rate or frequency with respect to the data acquisition time. The complex cross-correlation function yields real and imaginary components that contain information about the phase behavior of the variables. The real component provides information about mutually dependent in-phase variations. Variations that occur out-of-phase (with time lags or leads) are given by the imaginary component. Two-dimensional correlation analysis is a general analysis method that can be used for the treatment of data from a variety of applications including image, distribution, environmental, and kinetic analysis.