• Journal of the Chungcheong Mathematical Society
• /
• v.37 no.1
• /
• pp.41-55
• /
• 2024

The nonconvex and nonsmooth optimization problem has been widely applicable in image processing and machine learning. In this paper, we propose an extension of the proximal iteratively reweighted ℓ₁ algorithm for nonconvex and nonsmooth minmization problem. We assume the co-coerciveness of a term of objective function instead of Lipschitz gradient condition, which is generalized property of Lipschitz continuity. We prove the global convergence of the proposed algorithm. Numerical results show that the proposed algorithm converges faster than original proximal iteratively reweighed algorithm and existing algorithms.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.13 no.8
• /
• pp.3962-3980
• /
• 2019

To deal with single sample face recognition, this paper presents a patch based semi-supervised linear regression (PSLR) algorithm, which draws facial variation information from unlabeled samples. Each facial image is divided into overlapped patches, and a regression model with mapping matrix will be constructed on each patch. Then, we adjust these matrices by mapping unlabeled patches to $[1,1,{\cdots},1]^T$. The solutions of all the mapping matrices are integrated into an overall objective function, which uses ${\ell}_{2,1}$-norm minimization constraints to improve discrimination ability of mapping matrices and reduce the impact of noise. After mapping matrices are computed, we adopt majority-voting strategy to classify the probe samples. To further learn the discrimination information between probe samples and obtain more robust mapping matrices, we also propose a multistage PSLR (MPSLR) algorithm, which iteratively updates the training dataset by adding those reliably labeled probe samples into it. The effectiveness of our approaches is evaluated using three public facial databases. Experimental results prove that our approaches are robust to illumination, expression and occlusion.