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Canonical correlation analysis (CCA) describes the associations between twosets of variables by maximizing the correlation between linear combinations ofthe variables in each data set. However, in high-dimensional settings where thenumber of variables exceeds the sample size or when the variables are highlycorrelated, traditional CCA is no longer appropriate. This paper proposes amethod for sparse CCA. Sparse estimation produces linear combinations of only asubset of variables from each data set, thereby increasing the interpretabilityof the canonical variates. We consider the CCA problem from a predictive pointof view and recast it into a regression framework. By combining an alternatingregression approach together with a lasso penalty, we induce sparsity in thecanonical vectors. We compare the performance with other sparse CCA techniquesin different simulation settings and illustrate its usefulness on a genomicdata set.

Sparse canonical correlation analysis from a predictive point of view