  In this paper, we propose the Lipschitz margin ratio and a new metric
learning framework for classification through maximizing the ratio. This
framework enables the integration of both the inter-class margin and the
intra-class dispersion, as well as the enhancement of the generalization
ability of a classifier. To introduce the Lipschitz margin ratio and its
associated learning bound, we elaborate the relationship between metric
learning and Lipschitz functions, as well as the representability and
learnability of the Lipschitz functions. After proposing the new metric
learning framework based on the introduced Lipschitz margin ratio, we also
prove that some well known metric learning algorithms can be shown as special
cases of the proposed framework. In addition, we illustrate the framework by
implementing it for learning the squared Mahalanobis metric, and by
demonstrating its encouraging results on eight popular datasets of machine
learning.
