Margin distribution explanation on metric learning for nearest neighbor classification

The importance of metrics in machine learning and pattern recognition algorithms has led to an increasing interest for optimizing distance metrics in recent years. Most of the state-of-the-art methods focus on learning Mahalanobis distances and the learned metrics are in turn heavily used for the nearest neighbor-based classification (NN). However, until now no theoretical link has been established between the learned metrics and their performance in NN. Although some existing methods such as large-margin nearest neighbor (LMNN), have employed the concept of large margin to learn a data-dependent metric, the link between the margin and the generalization performance for the metric is not fully understood. Though the recent work has indeed provided tenable margin distribution explanation on Boosting, the margin used in metric learning is quite different from that in Boosting. Thus, in this paper we try to analyze the effectiveness of metric learning algorithms for NN from the perspective of the margin distribution and provide a general and effective evaluation criterion for metric learning. On the one hand, we derive the generalization error upper bound for NN with respect to the Mahalanobis metric. On the other hand, the experiments on several benchmark datasets using existing metric learning algorithms demonstrate that large margin distribution can be obtained by these algorithms. Motivated by our analysis above, we also present a novel margin based metric learning algorithm for NN, which explicitly enlarges the margin distribution on various datasets and achieves very competitive results with the existing metric learning algorithms.