  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.
