Binary- and Multi-class Group Sparse Canonical Correlation Analysis for Feature Extraction and Classification

This paper incorporates the group sparse representation into the well-known canonical correlation analysis (CCA) framework and proposes a novel discriminant feature extraction technique named group sparse canonical correlation analysis (GSCCA). GSCCA uses two sets of variables and aims at preserving the group sparse (GS) characteristics of data within each set in addition to maximize the global interset covariance. With GS weights computed prior to feature extraction, the locality, sparsity and discriminant information of data can be adaptively determined. The GS weights are obtained from an NP-hard group-sparsity promoting problem that considers all highly correlated data within a group. By defining one of the two variable sets as the class label matrix, GSCCA is effectively extended to multiclass scenarios. Then GSCCA is theoretically formulated as a least-squares problem as CCA does. Comparative analysis between this work and the related studies demonstrate that our algorithm is more general exhibiting attractive properties. The projection matrix of GSCCA is analytically solved by applying eigen-decomposition and trace ratio (TR) optimization. Extensive benchmark simulations are conducted to examine GSCCA. Results show that our approach delivers promising results, compared with other related algorithms.