In Canonical Correlation Analysis (CCA), we have two sets of column vectors $X = \{x_1, x_2 ... x_n \}$ and $Y = \{y_1, y_2 ... y_n \}$ and find the linear combinations of each set, says $a = \Sigma_i a_ix_i$ and $b = \Sigma_i b_iy_i$ such that $a$ and $b$ has the maximal correlation.
My question is, if we are given only one set of column vectors $X = \{x_1, x_2 ... x_n \}$, is there an algorithm to divide $X$ into two groups such that after CCA on these two groups, the correlation is the largest?
(without enumerating all $2^n$ possibilities and excluding the trivial case when $X$ is rank deficient.)
Thanks.