## Nguyen Thai An, Pham Dinh Dong, Xiaolong Qin, Robust feature selection via nonconvex sparsity-based methods

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DOI: 10.23952/jnva.5.2021.1.05

Volume 5, Issue 1, 1 February 2021, Pages 59-77

Abstract. In this paper, we propose a new model for supervised multiclass feature selection which has the $\ell_{2,1}$-norm in both the fidelity loss and the regularization terms with an additional $\ell_{2,0}$-constraint. This problem is challenging for applying available optimization methods because of the discontinuous and nonconvex nature of the $\ell_{2,0}$-norm. We first convert the constraint defined by the $\ell_{2,0}$-norm into a new constraint defined by a difference of two matrix norms. Then we reformulate the problem as an unconstrained problem using the exact penalty method. Based on a derived formula for the proximal mapping of this difference of matrix norms and Nesterov’s smoothing techniques, the nonmonotonic accelerated proximal gradient method is applied to solve the unconstrained problem. Numerical experiments are conducted on many benchmark data sets to show the effectiveness of our proposed method in comparison with existing methods.