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. Classical and sparse Canonical correlation analysis (CCA) models consider the contribution of all the samples of data matrices and thus cannot identify an underlying specific subset of samples. We propose a novel Sparse weighted canonical correlation analysis (SWCCA), where weights are used for regularizing different samples. We solve the L₀-regularized SWCCA (L₀-SWCCA) using an alternating iterative algorithm. We apply L₀-SWCCA to synthetic data and real-world data to demonstrate its effectiveness and superiority compared to related methods. We consider also SWCCA with different penalties like Least absolute shrinkage and selection operator (LASSO) and Group LASSO, and extend it for integrating more than three data matrices.