Support vector machines (SVM) is very efficient and popular tool for classification, however, its non-robustness to outliers is a critical drawback. In fact, SVM is more sensitive to outliers than other classifiers since the optimal separating hyperplane obtained by SVM is solely determined by support vectors. So far all the studies about outliers in SVM are done by trying to minimize the effect of outliers by specifying robust loss functions. In this paper, we propose a version of Cook’s distance based on the deletion method and the infinitesimal perturbation method. Also, we express the Cook’s distance in terms of basic building blocks such as residual and leverage. Further, we propose a simple measure which can be used as either descriptive statistics in SVM diagnostics or approximate measure when the Cook’s distance cannot be computed due to the high-dimensionality.

中文翻译：

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支持向量机中的影响诊断

支持向量机（SVM）是非常有效且流行的分类工具，但是，其对异常值的鲁棒性是一个关键缺点。实际上，由于SVM获得的最佳分离超平面仅由支持向量确定，因此SVM比其他分类器对异常值更敏感。到目前为止，所有关于SVM离群值的研究都是通过尝试通过指定鲁棒损失函数来最大程度地减少离群值的影响而完成的。在本文中，我们提出了一种基于删除方法和无穷微扰动方法的库克距离版本。另外，我们用残差和杠杆等基本构成要素来表示库克的距离。进一步，