Sparse canonical covariance analysis for high-throughput data

Canonical covariance analysis (CCA) has gained popularity as a method for the analysis of two sets of high-dimensional genomic data. However, it is often difficult to interpret the results because canonical vectors are linear combinations of all variables, and the coefficients are typically nonzero. Several sparse CCA methods have recently been proposed for reducing the number of nonzero coefficients, but these existing methods are not satisfactory because they still give too many nonzero coefficients. In this paper, we propose a new random-effect model approach for sparse CCA; the proposed algorithm can adapt arbitrary penalty functions to CCA without much computational demands. Through simulation studies, we compare various penalty functions in terms of the performance of correct model identification. We also develop an extension of sparse CCA to address more than two sets of variables on the same set of observations. We illustrate the method with an analysis of the NCI cancer dataset.