In the era of big data, feature selection is indispensable as a dimensional reduction technique to lower data complexity and enhance machine learning performances. However, traditional feature selection methods mainly focus on classification performances, while they exclude the impact of associated feature costs; e.g., price, risk, and computational complexity for feature acquisition. In this research, we extend the ${\ell }_1$ norm support vector machine (${\ell }_1$-SVM) to address the feature costs, by incorporating a budget constraint to preserve classification accuracy with the least expensive features. Furthermore, we formulate its robust counterpart to address the uncertainty of the feature costs. To enhance computational efficiency, we also develop an algorithm to tighten the bound of the weight vector in the budget constraint. Through the experimental study on a variety of benchmark and synthetic datasets, our proposed mixed integer linear programming (MILP) models show that they can achieve competitive outcomes in terms of predictive and economic performances. Also, the algorithm that tightens the budget constraint helps to curtail computational complexity.

在大数据时代，特征选择作为降维技术必不可少，以降低数据复杂性并提高机器学习性能。然而，传统的特征选择方法主要关注分类性能，而它们却排除了相关特征成本的影响。例如，价格，风险和特征获取的计算复杂度。在这项研究中，我们扩展了${\ell }_{\mathrm{1个}}$ 规范支持向量机（${\ell }_{\mathrm{1个}}$-SVM）以解决功能成本，方法是合并预算约束以使用最便宜的功能保持分类准确性。此外，我们制定了其强大的对应物以解决特征成本的不确定性。为了提高计算效率，我们还开发了一种算法来收紧预算约束中权重向量的边界。通过对各种基准数据集和综合数据集的实验研究，我们提出的混合整数线性规划（MILP）模型表明，它们可以在预测和经济表现方面取得竞争性成果。而且，收紧预算约束的算法有助于减少计算复杂性。