Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Viet Nam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam.
Université de Lorraine, LGIPM, F-57000 Metz, France.
Neural Netw. 2019 Oct;118:220-234. doi: 10.1016/j.neunet.2019.05.011. Epub 2019 Jul 4.
The need to select groups of variables arises in many statistical modeling problems and applications. In this paper, we consider the ℓ-norm regularization for enforcing group sparsity and investigate a DC (Difference of Convex functions) approximation approach for solving the ℓ-norm regularization problem. We show that, with suitable parameters, the original and approximate problems are equivalent. Considering two equivalent formulations of the approximate problem we develop DC programming and DCA (DC Algorithm) for solving them. As an application, we implement the proposed algorithms for group variable selection in the optimal scoring problem. The sparsity is obtained by using the ℓ-regularization that selects the same features in all discriminant vectors. The resulting sparse discriminant vectors provide a more interpretable low-dimensional representation of data. The experimental results on both simulated datasets and real datasets indicate the efficiency of the proposed algorithms.
在许多统计建模问题和应用中，都需要选择变量组。本文考虑了 ℓ-norm 正则化以实现组稀疏性，并研究了一种用于解决 ℓ-norm 正则化问题的 DC（凸函数差）逼近方法。我们证明了，在适当的参数下，原始问题和近似问题是等价的。考虑到近似问题的两个等价形式，我们为其开发了 DC 规划和 DCA（DC 算法）来进行求解。作为应用，我们在最优评分问题中实现了所提出的用于组变量选择的算法。通过使用在所有判别向量中选择相同特征的 ℓ-正则化，得到稀疏性。生成的稀疏判别向量为数据提供了更具可解释性的低维表示。在模拟数据集和真实数据集上的实验结果表明了所提出算法的有效性。
