LAUSR

Regression analysis has been widely used for face recognition. This paper mainly discuss the following regularized matrix regression problem: Given a set of k image matrices and an image matrix find such that where are also a set of representation coefficients, λ is the model parameter, and represents the Frobenius norm of matrix A. Yuan and Liao [S.F. Yuan, A.P. Liao, Least squares Hermitian solution of the complex matrix equation AXB + CXD = E with the least norm. J. Frankl. Inst. 351 (2014), pp. 4978–4997] introduced a new product for matrices and vectors, and solved the least squares Hermitian problem of complex matrix equation In this paper, we deeply investigate this product and its relative properties about matrix trace, norm, and determinant. We then provide a direct method to get the close form solution for solving the regularized image matrix regression problem in face recognition.