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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 A 1 , A 2 , ... , A k ∈ R m × n and an image matrix B ∈ R m × n , find x = (x 1 , x 2 , ... , x k) T ∈ R k such that min x ∈ R k ∥ x 1 A 1 + x 2 A 2 + ⋯ + x k A k − B ∥ F 2 + λ 2 ∥ x ∥ 2 2 , where x 1 , x 2 , ... , x k are also a set of representation coefficients, λ is the model parameter, and ∥ A ∥ F 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 A X B + C X D = E. 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. [ABSTRACT FROM AUTHOR]

With the popularity of automobile, traffic safety and our lives are inseparable. In vehicular ad hoc networks (VANETs), the properties authenticity, privacy and traceability have already been considered in many previous researches. Many automotive systems combine their applications with smart life. In this paper, a speedy seamless safe (3-S) messaging mechanism for roadside-to-vehicle authentication and vehicle-to-vehicle communication is proposed. In addition to the essential requirements mentioned above, 3-S messaging mechanism is designed to reduce the computation cost and provide the seamless communication when the vehicle crosses the various regions. With better performance and availability, our scheme can be applied in various VANET applications, especially in safety systems to provide the drivers active safety. [ABSTRACT FROM AUTHOR]