Canonical Correlation Analysis

A glance at our friend here reveals the rounded head of the Celt, which carries inside it the Celtic enthusiasm and power of attachment. Dr. Mortimer in “The Hound of the Baskervilles” The association between two sets of variables may be quantified by canonical correlation analysis (CCA). Given a set of variables X ∈ Rq and another set Y ∈ Rp, one asks for the linear combination a_X that “best matches” a linear combination b_Y. The best match in CCA is defined through maximal correlation. The task of CCA is therefore to find a ∈ Rq and b ∈ Rp so that the correlation ρ(a, b) = ρa_X,b_Y is maximized. These best-matching linear combinations a_X and b_Y are then called canonical correlation variables; their correlation is the canonical correlation coefficient. The coefficients a and b of the canonical correlation variables are the canonical vectors.