Binary- and multi-class group sparse canonical correlation analysis for discriminant feature extraction and classification

Abstract

This paper incorporates the 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 to keep the group sparse (GS) characteristics of data within each set in addition to maximizing the global inter-set 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 calculated from a 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 multi-class case. Then GSCCA is theoretically formulated as a least squares problem. Comparative analysis between this work and other related work demonstrate that our approach is more general exhibiting attractive properties. The GSCCA projection matrix is analytically solved by using 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.