Statistical methods correlation between many data sets

Correlation methods provide many opportunities to help identify metabolites in NMR spectra by relating and/or isolating peaks from the same metabolites. A number of papers describe the application of correlation to NMR data. The method, popularly known as STOCSY (statistical total correlation spectros-copy), generates correlation coefficients between every pair of ID NMR peaks. Metabolites are identified based on the set of peaks with high correlations (126-129). Generally, in STOCSY, the correlation analysis is derived from all the ID NMR spectra from different samples in a dataset the 2D map of correlations obtained enables easy visualization of all correlations... 

In addition to the conventional spectral analysis methods and chemometrics, two-dimensional (2D) correlation spectroscopy has recently been introduced to NIR spectroscopy (4,12-16). In this method spectral peaks are spread over a second dimension to simplify the visualization of complex spectra consisting of many overlapped bands and to explore correlation between the bands. There are two kinds of 2D correlation spectroscopy used in NIR spectroscopy. One is statistical 2D correlation proposed originally by Barton et al (16). This method employs cross-correlation based on the least-squares linear regression analysis to assess spectral changes in two regions, such as the NIR and mid-IR regions, that arise from variations in sample composition (16). In another 2D correlation spectroscopy proposed by Noda (12, 13), 2D spectra are constructed from a set of spectral data collected from a system under an external physical perturbation, which induces selective alterations in spectral features. 

During the last two or three decades atomic spectroscopists have become used to the application of computers to control their instruments, develop analytical methods, analyse data and, consequently, to apply different statistical methods to explore multivariate correlations between one or more output(s) e.g. concentration of an analyte) and a set of input variables e.g. atomic intensities, absorbances). On the other hand, the huge efforts made by atomic spectroscopists to resolve interferences and optimise the instrumental measuring devices to increase accuracy and precision have led to a point where many of the difficulties that have to be solved nowadays cannot be described by simple univariate linear regression methods (Chapter 1 gives an extensive review of some typical problems shown by several atomic techniques). Sometimes such problems cannot even be addressed by multivariate regression methods based on linear relationships, as is the case for the regression methods described in the previous two chapters. 

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