Covariance mapping analysis

The power of covariance mapping will be illustrated by one example. When Lavancier et al. [21] studied the multiple ionization of CO at 305 nm, analysis of their conventional TOP spectra suggested that the process [CO ]-+ + O... 

Shen, P Hauri, D. Ross, J. Oefner, P. J. Analysis of glycolysis metabolites by capillary zone electrophoresis with indirect UV detection.7. Capillary Electrophor. 1996,3,155-163. Card, D. A. Fohner, D. E. Sato, S. Buzza, S. A. Castleman, A. W., Jr. Covariance mapping of ammonia clusters evidence of the coimectiveness of clusters with coulombic explosion. J. Phys. Chem. 1997,101, 3417-3423. 

Covariance NMR mostly refers to any NMR experiment whose resulting data are subjected at some point to covariance analysis, covariance transformation or covariance treatment. Covariance NMR processing describes the steps that compute the covariance from a matrix of NMR data and yields the covariance map. The covariance map is equivalent to a NMR spectrum obtained after Fourier transformation, if the covariance was calculated obeying certain mathematical constraints, cf further below. In other words. 

Figure 7 Combined data analysis in x- and y-space. J> and J>2 are orthogonal projection axes in x-space, y i and 2 are orthogonal projection axes in y-space. If the method CCA is used for the determination of the.se latent variables the scores u for j,b and y i have the maximum possible correlation coefficient if PLS is used they have the maximum possible covariance. Mapping of x-space is influenced by y-data, and vice versa. Regression models can be built between the. scores in x-space and in y-space...

Figure 3 presents the reconstructed mass spectrum of the first discriminant function which separated the river and marine stations in the DiD2-map of Figure 1. The positive D-function describes the covariant mass peaks with higher intensities with respect to the zero point spectrum. All sample spectra with such characteristics will have positive score values. This spectrum is a representation of the characteristics of riverine material. The negative D-function spectrum in Figure 3 is indicative of the marine characteristics. The D spectrum shows a number of mass peaks indicative for carbohydrates, lignin and proteinaceous material (12). The mass peak m/z=86 and 100 are uncommon and a special characteristic of these fluvial samples. It can be speculated to be the molecular ion of (alkyl)thiadiazole (a metal binding pollutant), however a cyclic ketone, short chain alcohol or unsaturated acid are also possibilities. These mass peaks were chosen for further study because of their rare occurrence and their high discriminating power in the factor-discriminant analysis.

In comparison to other spectroscopic techniques, where generahzed covariance was performed to obtain synchronous and asynchronous correlation maps and where both correlation maps were interpreted, the asynchronous map was rarely exploited if considered at aU for NMR purposes. Yet, the synchronous map as an equivalent to the direct covariance spectrum served to correlate species in different samples for a few studies. In contrast, analysis of the sample variation by statistical total correlation NMR, STOCSY, has become a comer stone of metabolomics investigations this field was considered beyond the scope of this chapter, hence only the current variants of STOCSY and their purposes were briefly presented. 

R. Selvaratnam, S. Chowdhury, S.B. Van, G. Melacini, Mapping allostery through the covariance analysis of NMR chemical shifts, Proc. Natl. Acad. Sci. U.S.A. (2011) 1. 

This discussion will focus on two main techniques to perform the reduction (1) principal component analysis and (2) factor analysis. Both of these techniques attempt to find an appropriate low-dimensional representation of the covariance matrix. Other approaches such as multi-dimensional scaling, non-linear mapping, and Kohonen networks are reviewed briefly in this section, and discussed in greater detail in Section 5. 

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