What Makes Objects Similar: A Unified Multi-Metric Learning Approach

Linkages are essentially determined by similarity measures that may be derived from multiple perspectives. For example, spatial linkages are usually generated based on localities of heterogeneous data. Semantic linkages, however, can come from even more properties, such as different physical meanings behind social relations. Many existing metric learning models focus on spatial linkages but leave the rich semantic factors unconsidered. We propose a Unified Multi-Metric Learning framework to exploit multiple types of metrics with respect to overdetermined similarities between linkages. In , a type of combination operator is introduced for distance characterization from multiple perspectives, and thus can introduce flexibilities for representing and utilizing both spatial and semantic linkages. Besides, we propose a uniform solver for , and the theoretical analysis reflects the generalization ability of as well. Extensive experiments on diverse applications exhibit the superior classification performance and comprehensibility of . Visualization results also validate its ability on physical meanings discovery.