  We consider the problem of sparse canonical correlation analysis (CCA), i.e.,
the search for two linear combinations, one for each multivariate, that yield
maximum correlation using a specified number of variables. We propose an
efficient numerical approximation based on a direct greedy approach which
bounds the correlation at each stage. The method is specifically designed to
cope with large data sets and its computational complexity depends only on the
sparsity levels. We analyze the algorithm's performance through the tradeoff
between correlation and parsimony. The results of numerical simulation suggest
that a significant portion of the correlation may be captured using a
relatively small number of variables. In addition, we examine the use of sparse
CCA as a regularization method when the number of available samples is small
compared to the dimensions of the multivariates.
