The support vector machine (SVM) is a well-established classification method whose name refers to the particular training examples, called support vectors, that determine the maximum margin separating hyperplane. The SVM classifier is known to enjoy good generalization properties when the number of support vectors is small compared to the number of training examples. However, recent research has shown that in sufficiently high-dimensional linear classification problems, the SVM can generalize well despite a proliferation of support vectors where all training examples are support vectors. In this paper, we identify new deterministic equivalences for this phenomenon of support vector proliferation, and use them to (1) substantially broaden the conditions under which the phenomenon occurs in high-dimensional settings, and (2) prove a nearly matching converse result.

中文翻译：

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关于高维支持向量的扩散

支持向量机 (SVM) 是一种行之有效的分类方法，其名称是指特定的训练示例，称为支持向量，用于确定最大间隔分离超平面。众所周知，当支持向量的数量与训练示例的数量相比较小时，SVM 分类器具有良好的泛化特性。然而，最近的研究表明，在足够高维的线性分类问题中，尽管所有训练示例都是支持向量的支持向量激增，但 SVM 可以很好地泛化。在本文中，我们为这种支持向量增殖现象确定了新的确定性等价物，并使用它们来（1）显着拓宽该现象在高维设置中发生的条件，