Multi-granularity distance metric learning via neighborhood granule margin maximization

Learning a distance metric from training samples is often a crucial step in machine learning and pattern recognition. Locality, compactness and consistency are considered as the key principles in distance metric learning. However, the existing metric learning methods just consider one or two of them. In this paper, we develop a multi-granularity distance learning technique. First, a new index, neighborhood granule margin, which simultaneously considers locality, compactness and consistency of neighborhood, is introduced to evaluate a distance metric. By maximizing neighborhood granule margin, we formulate the distance metric learning problem as a sample pair classification problem, which can be solved by standard support vector machine solvers. Then a set of distance metrics are learned in different granular spaces. The weights of the granular spaces are learned through optimizing the margin distribution. Finally, the decisions from different granular spaces are combined with weighted voting. Experiments on UCI datasets, gender classification and object categorization tasks show that the proposed method is superior to the state-of-the-art distance metric learning algorithms.