5 There are also several extensions of PCA that are useful if, for example, one wishes to emphasize some variables over others, such as weighted PCA, 3, 6 or if a non-linear model of the data is appropriate, such as generalized PCA. 3 It is widely applied in pattern classification and is used, for example, in such diverse fields as drug discovery 4 and face recognition. One of the most useful such strategies is the principal component analysis (PCA), 2 a multivariate technique in which a linear projection is used to transform data into a smaller set of uncorrelated variables. 1 For this purpose, several different strategies are utilized to highlight significant correlations among the relevant variables. One goal of data analytics is the effective dimensional reduction of large, high-dimensional data sets by the identification of a few low-dimensional axes that are most important. Finally, we describe how this approach facilitates experimental planning and process control. We demonstrate that our approach leads to a substantial enhancement of correlations, as illustrated by two experimental applications of substantial interest to the materials science community, namely: (1) determining the interdependence of processing and microstructural variables associated with doped polycrystalline aluminas, and (2) relating microstructural decriptors to the electrical and optoelectronic properties of thin-film solar cells based on CuInSe 2 absorbers. With this in mind, we describe here a versatile, Monte-Carlo based methodology that is useful in identifying non-linear functions of the variables that lead to strong input/output correlations. One shortcoming of the canonical correlation analysis, however, is that it provides only a linear combination of variables that maximizes these correlations. It is especially useful in data analytics as a dimensional reduction strategy that simplifies a complex, multidimensional parameter space by identifying a relatively few combinations of variables that are maximally correlated. A canonical correlation analysis is a generic parametric model used in the statistical analysis of data involving interrelated or interdependent input and output variables.

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