Dual approximated nuclear norm based matrix regression via adaptive line search scheme

摘要

Face recognition with partial occlusion is one of the urgent and challenging problems in the pattern recognition research. Using the Alternating Direction Method of Multipliers (ADMM), the recently proposed nuclear norm based matrix regression model (NMR) has been shown a great potential in dealing with the structural noise. And yet, ADMM needs to bring into an auxiliary variable and only exploits the convexity of NMR. Compared with ADMM, the gradient based methods are simpler. To make use of these methods, this paper considers the Approximated NMR (ANMR) model. Utilizing the singular value shrinkage operator and strong convexity of ANMR, the dual problem of ANMR (DANMR) is derived and a crucial result is obtained: the primal optimal solution of ANMR can be converted as the matrix function associated with the dual optimal solution. Due to the differentiability of DANMR, an adaptive line search scheme is developed to solve it. This approach combines the advantages of the accelerated gradient technique and adaptive parameters updating strategy. Therefore, a convergence rate of O(1/N2) can be guaranteed. Experimental results show the superiority of the proposed algorithm over some existing methods.