论文标题
在高维度中支持向量的扩散
On the proliferation of support vectors in high dimensions
论文作者
论文摘要
支持向量机（SVM）是一种良好的分类方法，其名称是指确定超平面分离超平面的最大边距分离的特定训练示例。与培训示例相比，当支持向量的数量少时，SVM分类器享有良好的概括属性。但是，最近的研究表明，在足够高的线性分类问题中，尽管支持向量的扩散，但在所有训练示例都是支持向量的情况下，SVM可以很好地概括。在本文中，我们确定了这种支持矢量增殖现象的新的确定性等效性，并使用它们来（1）实质上扩大了该现象在高维环境中发生的条件，并且（2）证明了几乎匹配的逆向结果。
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.
