With the rapid development of new genetic measurement methods, several types of genetic alterations can be quantified in a high-throughput manner. While the initial focus has been on investigating each data set separately, there is an increasing interest in studying the correlation structure between two or more data sets. Multivariate methods based on Canonical Correlation Analysis (CCA) have been proposed for integrating paired genetic data sets. The high dimensionality of microarray data imposes computational difficulties, which have been addressed for instance by studying the covariance structure of the data, or by reducing the number of variables prior to applying the CCA. In this work, we propose a new method for analyzing high-dimensional paired genetic data sets, which mainly emphasizes the correlation structure and still permits efficient application to very large data sets. The method is implemented by translating a regularized CCA to its dual form, where the computational complexity depends mainly on the number of samples instead of the number of variables. The optimal regularization parameters are chosen by cross-validation. We apply the regularized dual CCA, as well as a classical CCA preceded by a dimension-reducing Principal Components Analysis (PCA), to a paired data set of gene expression changes and copy number alterations in leukemia.