Joint diagonalization for a pair of Hermitian quaternion matrices and applications to color face recognition

Abstract

A new joint diagonalization algorithm for a pair of Hermitian quaternion matrices is derived incorporating real structure-preserving strategy. The structure-preserving joint diagonalization algorithm leads to a novel two-dimensional quaternion linear discriminant analysis (2D-QLDA) method for color face recognition and image reconstruction. 2D-QLDA is mathematically characterized by Hermitian quaternion generalized eigenvalue problem. A weighted norm is obtained as a new measurement to determine the distances among Fisher feature matrices, which helps us avoid generating projected images explicitly. Numerical results based on the real face databases indicate that 2D-QLDA performs better than other 2D-LDA-like methods in color face recognition and is effective in image reconstruction.