Analysis maximum redundancy

The use of these latent variables provides PLS with a greater capacity than MLR to distill most of the information contained in a large number of descriptors and properties into a smaller number of factors and thereby avoid some of the ravages of the Curse of Dimensionality. It is especially suited to dealing with systems containing many highly correlated descriptors. PLS is related to the methods of principal components analysis (PCA) and maximum redundancy analysis (MRA), in that all three methods augment the raw desaiptors with matrices derived from variance found in the descriptors themselves (PCA), the properties to be modeled (MRA), or a combination of both (PLS). ... 

The simplest and most widely used chemometric technique is Principal Component Analysis (PCA). Its objective is to accomplish orthogonal projection and in that process identify the minimum number of sensors yielding the maximum amount of information. It removes redundancies from the data and therefore can be called a true data reduction tool. In the PCA terminology, the eigenvectors have the meaning of Principal Components (PC) and the most influential values of the principal component are called primary components. Another term is the loading of a variable i with respect to a PQ. 

Similar to approach given by Coit (Coit 2003) the analysis as demonstrated in figure 5, suggests that there is a maximal limit which the cold redundancy offers better reliability than active redundancy. Above of the maximal limit, the active redundancy will be eh-gible. Due to overall cost restraint (c=200), deploying more than two redundant components for each element is not considered in the given example. The maximum defined number of components within a subsystem has been defined 2. 

From the data analytical standpoint, multiway arrays represent a particularly rich source of information, as they often contain a large degree of redundancy, because many signals are used to describe a single sample. Accordingly, specific mathematical and statistical tools have been developed over the years to take the maximum advantage from the analysis of these kinds of data in this respect, multiway analysis is nothing else than the analysis of multiway data [6,7]. However, its main characteristic is that, due to the peculiarity of the data structures involved, it makes use of tools which are somewhat different from, even if in some cases related to, the standard methods used for the analysis of two-way data, such as the ones discussed in Chapters 3-5. 

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