Canonical correlation analysis (CCA) is a widely used multivariate analysis technique for explaining the relation between two sets of variables. It achieves this goal by finding linear combinations of the variables with maximal correlation. Recently, under the assumption that leading canonical directions are sparse, various penalized CCA procedures have been proposed for high dimensional data applications. However, all these procedures have the inconvenience of not preserving the sparsity among the retained leading canonical directions. To address this issue, two new sparse CCA methods are proposed in this paper. The first method is obtained by diagonal thresholding of two square matrices derived from the cross-covariance matrix of the two sets of variables where each matrix characterizes one set of variables. A model selection criterion is used to select the number of variables to retain from each matrix diagonal. The second method is derived within an adaptive alternating penalized least squares framework where the 1 2-norm is used as a penalty promoting block sparsity. Compared to existing sparse CCA methods, the proposed methods have the advantage of preserving the sparsity across the retained canonical loading vectors. Their performance are illustrated in an extended experimental study which shows the superior performance of the proposed methods.

Canonical correlation analysis (CCA) describes the relationship between two sets of variables by finding linear combinations of the variables with maximal correlation. Recently, under the assumption that the leading canonical correlation directions are sparse, various procedures have been proposed for many high-dimensional applications to improve the interpretability of CCA. However all these procedures have the inconvenience of not preserving the sparsity among the retained leading canonical directions. To address this issue, a new sparse CCA method is proposed in this paper. It is derived within a penalized alternative least squares framework where the 12-norm is used as a penalty promoting block sparsity. The proposed method has the advantage of generating the same sparsity pattern across all retained canonical correlation components. The performance of the proposed method is demonstrated in a simulation study.

Canonical correlation analysis (CCA) is a data driven method that has been successfully used in functional magnetic resonance imaging (fMRI) data analysis. Standard CCA extracts meaningful information from a data set by seeking pairs of linear combinations from two sets of variables with maximum pairwise correlation. So far, however, this method has been used without incorporating prior information available for fMRI data. In this paper, we address this issue by proposing a new CCA method named PCCA (for projection CCA). PCCA is obtained by using the discrete cosine transform (DCT) to create a basis for a span that better characterizes the fMRI data set. Employing DCT guides the estimated canonical variates, yielding a more computationally efficient CCA procedure. The proposed method can be seen as a regularized CCA method where regularization is introduced via basis expansion. The advantages of the proposed PCCA algorithm over the standard CCA are illustrated on both simulated data and real fMRI data from a resting state experiment.