Canonical correlation analysis (CCA) is a way of measuring the linear relationship between two multidimensional variables. It finds two bases, one for each variable, that are optimal with respect to correlations and, at the same time, it finds the corresponding correlations. In other words, it finds the two bases in which the correlation matrix between the variables is diagonal and the correlations on the diagonal are maximized. The dimensionality of these new bases is equal to or less than the smallest dimensionality of the two variables.
An important property of canonical correlations is that they are invariant with respect to affine transformations of the variables. This is the most important difference between CCA and ordinary correlation analysis which highly depend on the basis in which the variables are described.
CCA was developed by H. Hotelling [10]. Although being a standard tool in statistical analysis, where canonical correlation has been used for example in economics, medical studies, meteorology and even in classification of malt whisky, it is surprisingly unknown in the fields of learning and signal processing. Some exceptions are [2,13,5,4,14],
For further details and applications in signal processing, see my PhD thesis [3] and other publications.