Generalized Canonical Correlation Analysis Using GSVD

Canonical Correlation Analysis (CCA) is a well-known method for feature extraction and dimension reduction. CCA can simultaneously deal with two sets of data. It makes CCA can be used for feature level fusion. But it suffers the Small Sample Size (SSS) problem. In this paper, a new optimization criterion is presented for overcoming the SSS problem. The optimization problem can be solved analytically by applying the Generalized Singular Value Decomposition (GSVD) technique. We name our method GSVDCCA. But fusion based on CCA sacrifices the class discrimination information in the process of feature fusion. We propose generalized GSVDCCA (GGSVDCCA) fusion algorithm to overcome this limitation. This new method improves correlation criterion function by minimizing the within-class variation to enhance classification performance. From our experiment results on face and palm print database, we clearly find that not only the SSS problem can be effectively solved, but also better recognition performance has been achieved.