Metric Learning via Maximizing the Lipschitz Margin Ratio

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.