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. 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.ġ For this purpose, several different strategies are utilized to highlight significant correlations among the relevant variables. 3 It is widely applied in pattern classification and is used, for example, in such diverse fields as drug discovery 4 and face recognition. In many cases, one is interested in finding the correlations between two sets of variables.ĥ 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. For example, in an engineering application one may wish to find a connection between a set of processing variables (controlled by the engineer) and a set of output variables, the latter characterizing a product. A canonical correlation analysis (CCA) is a very general technique for quantifying relationships between two sets of variables, and most parametric tests of significance are essentially special cases of CCA. 8 In particular, for two paired data sets, a CCA identifies paired directions such that the projection of the first data set along the first direction is maximally correlated with the projection of the second data set along the second direction. 9 A reduction in dimensionality is achieved by identifying a subspace that best represents the data.

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