IEEE Trans Neural Netw Learn Syst. 2020 Jun;31(6):2217-2221. doi: 10.1109/TNNLS.2019.2927282. Epub 2019 Aug 7.
The generalized lasso (GLasso) is an extension of the lasso regression in which there is an l penalty term (or regularization) of the linearly transformed coefficient vector. Finding the optimal solution of GLasso is not straightforward since the penalty term is not differentiable. This brief presents a novel one-layer neural network to solve the generalized lasso for a wide range of penalty transformation matrices. The proposed neural network is proven to be stable in the sense of Lyapunov and converges globally to the optimal solution of the GLasso. It is also shown that the proposed neural solution can solve many optimization problems, including sparse and weighted sparse representations, (weighted) total variation denoising, fused lasso signal approximator, and trend filtering. Disparate experiments on the above problems illustrate and confirm the excellent performance of the proposed neural network in comparison to other competing techniques.
广义套索（GLasso）是套索回归的一种扩展，其中线性变换系数向量有一个 l 惩罚项（或正则化项）。由于惩罚项不可微，因此找到 GLasso 的最优解并不直接。本文提出了一种新颖的单层神经网络，用于解决广泛的惩罚变换矩阵的广义套索问题。所提出的神经网络在 Lyapunov 意义上是稳定的，并全局收敛到 GLasso 的最优解。还表明，所提出的神经网络解可以解决许多优化问题，包括稀疏和加权稀疏表示、（加权）全变差去噪、融合套索信号逼近器和趋势滤波。针对上述问题的不同实验说明了并证实了与其他竞争技术相比，所提出的神经网络的出色性能。
