Generalization analysis of multi-modal metric learning

Multi-modal metric learning has recently received considerable attention since many real-world applications involve multi-modal data. However, there is relatively little study on the generalization analysis of the associated learning algorithms. In this paper, we bridge this theoretical gap by deriving its generalization bounds using Rademacher complexities. In particular, we establish a general Rademacher complexity result by systematically analyzing the behavior of the resulting models with various regularizers, e.g., lp-regularizer on the modality level with either a mixed (q,s)-norm or a Schatten norm on each modality. Our results and the discussion followed help to understand how the prior knowledge can be exploited by selecting an appropriate regularizer.