Globality and locality incorporation in distance metric learning

Supervised distance metric learning plays a substantial role to the success of statistical classification and information retrieval. Although many related algorithms are proposed, it is still an open problem about incorporating both the geometric information (i.e., locality) and the label information (i.e., globality) in metric learning. In this paper, we propose a novel metric learning framework, called “Dependence Maximization based Metric Learning” (DMML), which can efficiently integrate these two sources of information into a unified structure as instances of convex programming without requiring balance weights. In DMML, the metric is trained by maximizing the dependence between data distributions in the reproducing kernel Hilbert spaces (RKHSs). Unlike learning in the existing information theoretic algorithms, however, DMML requires no estimation or assumption of data distributions. Under this proposed framework, we present two methods by employing different independence criteria respectively, i.e., Hilbert–Schmidt Independence Criterion and the generalized Distance Covariance. Comprehensive experimental results for classification, visualization and image retrieval demonstrate that DMML favorably outperforms state-of-the-art metric learning algorithms, meanwhile illustrate the respective advantages of these two proposed methods in the related applications.