As support vector machines (SVM) are used extensively in machine learning applications, it becomes essential to obtain a sparse model that is also robust to noise in the data set. Although many researchers have presented different approaches to get a robust SVM, the work on robust SVM based on rescaled hinge loss function (RSVM-RHHQ) has attracted a great deal of attention. The method of using correntropy with hinge loss function has added a noticeable amount of robustness to the model. However, the sparsity of the model can be further improved. In this work, we focus on enhancing the sparsity of RSVM-RHHQ. As this work is the improved version of the RSVM-RHHQ, we follow the same track (of adding noise in the data) of RSVM-RHHQ with altogether a new problem formulation. We apply correntropy to the \(\alpha \)-hinge loss function, which results in a better loss function than the rescaled hinge loss function. We use a non-smooth regularizer with a non-convex and non-smooth loss function. We solve this non-smooth and non-convex problem using the primal–dual proximal method. We find that this combination not only adds sparsity to the model, but it is also better than the existing robust SVM methods in terms of robustness towards label noise. We also provide the convergence proof of the proposed approach. In addition, the time complexity of the optimization technique is included. We perform experiments over various publicly available real-world data sets to compare the proposed method with the existing robust SVM methods. For experimentation purposes, we use small data sets, large data sets, and also data sets with significant class imbalance. Experimental results show that the proposed approach outperforms existing methods in sparseness, accuracy, and robustness. We also provide the sensitivity analysis of the regularization parameter for the label noise in the data set.

由于支持向量机（SVM）在机器学习应用中得到了广泛使用，因此获得对数据集中的噪声也具有鲁棒性的稀疏模型变得至关重要。尽管许多研究人员提出了获得鲁棒SVM的不同方法，但基于重新缩放的铰链损耗函数的鲁棒SVM的工作（RSVM-RHHQ）引起了很多关注。使用具有铰链损耗功能的肾上腺素的方法为模型增加了显着的鲁棒性。但是，可以进一步改善模型的稀疏性。在这项工作中，我们专注于增强RSVM-RHHQ的稀疏性。由于这项工作是RSVM-RHHQ的改进版本，因此我们遵循RSVM-RHHQ的相同轨道（在数据中添加噪声），并采用新的问题表述方式。我们将熵应用于\（\ alpha \）-铰链损耗函数，比重新缩放的铰链损耗函数产生更好的损耗函数。我们使用具有非凸和非平滑损失函数的非平滑正则化器。我们使用原始对偶近端方法解决了这个非光滑非凸的问题。我们发现这种组合不仅增加了模型的稀疏性，而且在对标签噪声的鲁棒性方面也优于现有的鲁棒SVM方法。我们还提供了该方法的收敛性证明。另外，还包括优化技术的时间复杂度。我们对各种可公开获得的现实世界数据集进行了实验，以将建议的方法与现有的鲁棒SVM方法进行比较。出于实验目的，我们使用小的数据集，大的数据集，以及具有严重的类不平衡的数据集。实验结果表明，该方法在稀疏性，准确性和鲁棒性方面优于现有方法。我们还提供了针对数据集中标签噪声的正则化参数的敏感性分析。