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This, however, cannot be verified unless multivariate approaches such as DPLS and UVE-DPLS are used.
Global multivariate approaches such as the proposed novel graph clustering correlation network are needed in order to understand the potential disregulation of normal cellular responses in disease and their response to various therapeutic interventions.
Multivariate approaches, such as principal component analysis or independent component analysis, decompose neuroimaging data into a set of spatial modes that capture the greatest amount of variance expressed over time, thereby identifying functional networks (Friston et al., 1993; Horwitz et al., 1998; Friston, 2002 b ; Fox and Raichle, 2007).
This method is especially relevant when a high between-subject variability is observed in repeated data: multivariate approaches (such as principal components analysis, PCA [ 19] and partial least square regressions, PLS [ 20]) can then be performed on X w to highlight the most relevant correlations between variables in the dataset, independently from individual variations.
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Other multivariate analysis approaches, such as biclustering or spectral analyses, might extend the possibilities of the method to identify the pathway profiles associated with a restricted number of samples and to fine-tune the network analysis to specific conditions within the experimental design.
There are also some multivariate non-parametric approaches, such as Wong et al's WSARE [ 17], which compares all possible groups defined by rules of a fixed length with their historic values.
For many such multivariate approaches, copulas and Sklar's theorem provide the mathematical background.
However, in photochemistry, by comparison, applications of such multivariate approaches were found to be less frequent although a variety of methods have been used, especially with spectroscopic photochemical applications.
Such multivariate approaches are now commonly used to understand how populations might respond to selection e.g. [ 7- 17, 17- 22].
The solution discussed also touches on the use of flexible analytic approaches, such as multivariate classification.
In addition, approaches such as multivariate source receptor modeling represent promising avenues for assessing exposure to complex mixtures (Hopke 2010), although further work is needed to account for key sources of uncertainty in such models.
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