An Efficient Newton-Based Method for Sparse Generalized Canonical Correlation Analysis

Generalized canonical correlation analysis (GCCA) that aims to deal with multi-view data has attracted extensive attention in signal processing. To improve the representation performance, this letter proposes a new sparsity constrained GCCA (SCGCCA). Technically, it integrates the $\ell _{2,0}$-norm constrained optimization into GCCA, which has not been investigated in the literature. Compared with the existing $\ell _{2,1}$-norm regularized GCCA, the proposed SCGCCA can not only exploit the similarity information belonging to the same features but also determine the number of extracted features. Although it is a nonconvex minimization problem, an efficient alternating minimization algorithm can be designed. Furthermore, a Newton hard thresholding pursuit technique is developed to accelerate the convergence tremendously. Empirical studies suggest both the effectiveness and efficiency of the proposed SCGCCA comparing with the existing GCCA and its variants. In particular, the speed can be increased by 150 times for the simulated dataset.