提出新型损失函数,让SVM更抗噪、更稳定,适合小样本高维数据。
Support Vector Machine Classifier with Rescaled Huberized Pinball Loss
- 用改进的非凸平滑损失设计新SVM模型,提升鲁棒性。
- 在多个数据集上表现优于传统SVM,尤其在噪声和小样本下优势明显。
- 理论严谨且可扩展,适合对稳定性要求高的实际应用。
支持向量机广泛用于分类任务,但传统模型对异常值敏感且重采样不稳定,限制了其实际应用。本文提出一种具有非对称性、非凸性和光滑性的新型重缩放赫伯-钉球损失函数,并基于此构建了RHPSVM(重缩放赫伯-钉球损失支持向量机)模型。理论分析表明,RHPSVM符合贝叶斯规则,具有严格的泛化误差界、有界影响函数和可控最优性条件,确保分类精度高、抗异常值能力强且重采样稳定。该模型可通过参数调整拓展为多种先进SVM变体,增强灵活性。采用凹凸规划(CCCP)将非凸优化问题转化为一系列凸子问题,并使用证明收敛的ClipDCD算法求解。在模拟数据、UCI数据集及小样本作物叶片图像分类任务上的实验结果表明,无论在有噪或无噪场景中,RHPSVM均优于现有SVM模型,尤其在处理高维小样本数据时表现突出。
原文摘要 · Abstract (English)
Support vector machines are widely used in machine learning classification tasks, but traditional SVM models suffer from sensitivity to outliers and instability in resampling, which limits their performance in practical applications. To address these issues, this paper proposes a novel rescaled Huberized pinball loss function with asymmetric, non-convex, and smooth properties. Based on this loss function, we develop a corresponding SVM model called RHPSVM (Rescaled Huberized Pinball Loss Support Vector Machine). Theoretical analyses demonstrate that RHPSVM conforms to Bayesian rules, has a strict generalization error bound, a bounded influence function, and controllable optimality conditions, ensuring excellent classification accuracy, outlier insensitivity, and resampling stability. Additionally, RHPSVM can be extended to various advanced SVM variants by adjusting parameters, enhancing its flexibility. We transform the non-convex optimization problem of RHPSVM into a series of convex subproblems using the concave-convex procedure (CCCP) and solve it with the ClipDCD algorithm, which is proven to be convergent. Experimental results on simulated data, UCI datasets, and small-sample crop leaf image classification tasks show that RHPSVM outperforms existing SVM models in both noisy and noise-free scenarios, especially in handling high-dimensional small-sample data.
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