Description of Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a method for searching for interactions between two data sets, the matrices X and Y. These data sets may have different numbers of features but the same number of objects. Using canonical analysis one creates a set of canonical variables / for the data set X and a set of canonical variables g for data set Y similar to the factors in factor analysis. The canonical variables / and g should have the following properties  

The starting point of analysis is the data matrix composed from X and Y  

One has now extracted synthetic variables which explain most of the interactions between the data sets X and Y. But in most cases one needs an interpretation of these canonical variables in relation to the original features  

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