1. A novel one-layer recurrent neural network for the l1-regularized least square problem
- Author
-
S. Hamid Mousavi, Majid Mohammadi, Wout Hofman, and Yao-Hua Tan
- Subjects
0301 basic medicine ,Lyapunov function ,Mathematical optimization ,Total variation ,Artificial neural network ,Computer science ,Cognitive Neuroscience ,Lyapunov ,Recurrent neural network ,Total variation denoising ,Convex ,Regularization (mathematics) ,Least squares ,Computer Science Applications ,03 medical and health sciences ,symbols.namesake ,030104 developmental biology ,Quadratic equation ,l-regularization ,Artificial Intelligence ,symbols ,Differentiable function ,Variable (mathematics) - Abstract
The l1-regularized least square problem has been considered in diverse fields. However, finding its solution is exacting as its objective function is not differentiable. In this paper, we propose a new one-layer neural network to find the optimal solution of the l1-regularized least squares problem. To solve the problem, we first convert it into a smooth quadratic minimization by splitting the desired variable into its positive and negative parts. Accordingly, a novel neural network is proposed to solve the resulting problem, which is guaranteed to converge to the solution of the problem. Furthermore, the rate of the convergence is dependent on a scaling parameter, not to the size of datasets. The proposed neural network is further adjusted to encompass the total variation regularization. Extensive experiments on the l1 and total variation regularized problems illustrate the reasonable performance of the proposed neural network.
- Published
- 2018