arXiv 2410.047742024-10cs.LG

粒球孪生支持向量机

Granular Ball Twin Support Vector Machine

Indian Institute of Technology Indore（印多尔印度理工学院）

A. Quadir, M. Sajid, M. Tanveer

备注：: Manuscript submitted to IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS: 19 September 2023; revised 13 February 2024 and 14 July 2024; accepted 05 October 2024
发表信息：: IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2024
DOI：: 10.1109/TNNLS.2024.3476391

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AI总结：

针对孪生支持向量机计算效率低、易过拟合且对噪声敏感的问题，提出以粒球为输入的GBTSVM及无需矩阵求逆并引入正则化的大规模LS-GBTSVM模型，显著提升了计算效率、鲁棒性与泛化能力。

摘要：

孪生支持向量机（TSVM）是一种新兴的机器学习模型，在分类和回归任务中具有广泛的应用性。然而，TSVM 面临着显著的挑战：$(i)$ 对矩阵求逆的迫切需求对其在大规模数据集上的效率和适用性构成了巨大障碍；$(ii)$ 在其原始公式中忽略了结构风险最小化（SRM）原则，加剧了过拟合风险；$(iii)$ TSVM 对噪声和异常值高度敏感，且在重采样时表现出不稳定性。鉴于上述挑战，我们提出了粒球孪生支持向量机（GBTSVM）。GBTSVM 以粒球而非单个数据点作为输入来构建分类器。这些粒球具有较粗的粒度，对重采样表现出鲁棒性，并降低了对噪声和异常值影响的敏感性。我们进一步提出了一种新型的大规模粒球孪生支持向量机（LS-GBTSVM）。LS-GBTSVM 的优化公式确保了两个关键方面：$(i)$ 它消除了矩阵求逆的需求，提升了 LS-GBTSVM 的计算效率；$(ii)$ 它通过引入正则化项纳入了 SRM 原则，有效解决了过拟合问题。所提出的 LS-GBTSVM 展现出对大型数据集的高效性、可扩展性以及对噪声和异常值的鲁棒性。我们在来自 UCI、KEEL 和 NDC 数据集的基准数据集上对 GBTSVM 和 LS-GBTSVM 模型进行了全面评估。我们的实验结果和统计分析证实了所提出的 GBTSVM 和 LS-GBTSVM 模型卓越的泛化能力。

英文摘要：

On Efficient and Scalable Computation of the Nonparametric Maximum Likelihood Estimator in Mixture ModelsTwin support vector machine (TSVM) is an emerging machine learning model with versatile applicability in classification and regression endeavors. Nevertheless, TSVM confronts noteworthy challenges: $(i)$ the imperative demand for matrix inversions presents formidable obstacles to its efficiency and applicability on large-scale datasets; $(ii)$ the omission of the structural risk minimization (SRM) principle in its primal formulation heightens the vulnerability to overfitting risks; and $(iii)$ the TSVM exhibits a high susceptibility to noise and outliers, and also demonstrates instability when subjected to resampling. In view of the aforementioned challenges, we propose the granular ball twin support vector machine (GBTSVM). GBTSVM takes granular balls, rather than individual data points, as inputs to construct a classifier. These granular balls, characterized by their coarser granularity, exhibit robustness to resampling and reduced susceptibility to the impact of noise and outliers. We further propose a novel large-scale granular ball twin support vector machine (LS-GBTSVM). LS-GBTSVM's optimization formulation ensures two critical facets: $(i)$ it eliminates the need for matrix inversions, streamlining the LS-GBTSVM's computational efficiency, and $(ii)$ it incorporates the SRM principle through the incorporation of regularization terms, effectively addressing the issue of overfitting. The proposed LS-GBTSVM exemplifies efficiency, scalability for large datasets, and robustness against noise and outliers. We conduct a comprehensive evaluation of the GBTSVM and LS-GBTSVM models on benchmark datasets from UCI, KEEL, and NDC datasets. Our experimental findings and statistical analyses affirm the superior generalization prowess of the proposed GBTSVM and LS-GBTSVM models.

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