Sparse Weighted Canonical Correlation Analysis

Given two data matrices $X$ and $Y$, sparse canonical correlation analysis (SCCA) is to seek two sparse canonical vectors $u$ and $v$ to maximize the correlation between $Xu$ and $Yv$. However, classical and sparse CCA models consider the contribution of all the samples of data matrices and thus cannot identify an underlying specific subset of samples. To this end, we propose a novel sparse weighted canonical correlation analysis (SWCCA), where weights are used for regularizing different samples. We solve the $L_0$-regularized SWCCA ($L_0$-SWCCA) using an alternating iterative algorithm. We apply $L_0$-SWCCA to synthetic data and real-world data to demonstrate its effectiveness and superiority compared to related methods. Lastly, we consider also SWCCA with different penalties like LASSO (Least absolute shrinkage and selection operator) and Group LASSO, and extend it for integrating more than three data matrices.