直觉模糊广义特征值近端支持向量机
Intuitionistic Fuzzy Generalized Eigenvalue Proximal Support Vector Machine
AI总结：
本文针对 GEPSVM 对噪声和异常值敏感的问题，提出 IF-GEPSVM 和 IF-IGEPSVM 两种直觉模糊模型，通过核函数为样本分配直觉模糊分数，并在多个数据集上验证了其优于基线模型的泛化性能和鲁棒性。
摘要：
广义特征值近端支持向量机（GEPSVM）因其结构简单、执行速度快和性能良好而受到广泛关注。GEPSVM 对所有样本赋予同等重要性，因此在面对包含噪声和异常值的真实世界数据集时，其鲁棒性和有效性会下降。为了减少噪声和异常值的影响，我们提出了一种新颖的直觉模糊广义特征值近端支持向量机（IF-GEPSVM）。所提出的 IF-GEPSVM 利用核函数，根据每个训练样本在高维特征空间中的位置和周围环境为其分配直觉模糊分数。IF-GEPSVM 优化问题的解通过求解广义特征值问题获得。此外，我们通过求解标准特征值分解提出了一种直觉模糊改进型 GEPSVM（IF-IGEPSVM），从而得到更简单、计算成本更低的优化问题，进而构建出高效的基于直觉模糊的模型。我们在 UCI 和 KEEL 数据集上对所提出的 IF-GEPSVM 和 IF-IGEPSVM 模型进行了全面评估。此外，为了评估所提出的 IF-GEPSVM 和 IF-IGEPSVM 模型的鲁棒性，我们在部分 UCI 和 KEEL 数据集中引入了标签噪声。实验结果表明，与现有基线模型相比，所提模型在有无标签噪声的情况下均展现出更优越的泛化性能。我们的实验结果在严格的统计分析支持下，证实了所提出的 IF-GEPSVM 和 IF-IGEPSVM 模型相对于基线模型具有更优越的泛化能力。此外，我们在 USPS 识别数据集上实现了所提出的 IF-GEPSVM 和 IF-IGEPSVM 模型，取得了有前景的结果，凸显了这些模型在实际和真实世界应用中的有效性。
英文摘要：
Generalized eigenvalue proximal support vector machine (GEPSVM) has attracted widespread attention due to its simple architecture, rapid execution, and commendable performance. GEPSVM gives equal significance to all samples, thereby diminishing its robustness and efficacy when confronted with real-world datasets containing noise and outliers. In order to reduce the impact of noises and outliers, we propose a novel intuitionistic fuzzy generalized eigenvalue proximal support vector machine (IF-GEPSVM). The proposed IF-GEPSVM assigns the intuitionistic fuzzy score to each training sample based on its location and surroundings in the high-dimensional feature space by using a kernel function. The solution of the IF-GEPSVM optimization problem is obtained by solving a generalized eigenvalue problem. Further, we propose an intuitionistic fuzzy improved GEPSVM (IF-IGEPSVM) by solving the standard eigenvalue decomposition resulting in simpler optimization problems with less computation cost which leads to an efficient intuitionistic fuzzy-based model. We conduct a comprehensive evaluation of the proposed IF-GEPSVM and IF-IGEPSVM models on UCI and KEEL datasets. Moreover, to evaluate the robustness of the proposed IF-GEPSVM and IF-IGEPSVM models, label noise is introduced into some UCI and KEEL datasets. The experimental findings showcase the superior generalization performance of the proposed models when compared to the existing baseline models, both with and without label noise. Our experimental results, supported by rigorous statistical analyses, confirm the superior generalization abilities of the proposed IF-GEPSVM and IF-IGEPSVM models over the baseline models. Furthermore, we implement the proposed IF-GEPSVM and IF-IGEPSVM models on the USPS recognition dataset, yielding promising results that underscore the models' effectiveness in practical and real-world applications.
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