Rethinking Maximum Mean Discrepancy for Visual Domain Adaptation

Existing domain adaptation approaches often try to reduce distribution difference between source and target domains and respect domain-specific discriminative structures by some distribution [e.g., maximum mean discrepancy (MMD)] and discriminative distances (e.g., intra-class and inter-class distances). However, they usually consider these losses together and trade off their relative importance by estimating parameters empirically. It is still under insufficient exploration so far to deeply study their relationships to each other so that we cannot manipulate them correctly and the model's performance degrades. To this end, this article theoretically proves two essential facts: 1) minimizing MMD equals to jointly minimizing their data variance with some implicit weights but, respectively, maximizing the source and target intra-class distances so that feature discriminability degrades and 2) the relationship between intra-class and inter-class distances is as one falls and another rises. Based on this, we propose a novel discriminative MMD with two parallel strategies to correctly restrain the degradation of feature discriminability or the expansion of intra-class distance; specifically: 1) we directly impose a tradeoff parameter on the intra-class distance that is implicit in the MMD according to 1) and 2) we reformulate the inter-class distance with special weights that are analogical to those implicit ones in the MMD and maximizing it can also lead to the intra-class distance falling according to 2). Notably, we do not consider the two strategies in one model due to 2). The experiments on several benchmark datasets not only prove the validity of our revealed theoretical results but also demonstrate that the proposed approach could perform better than some compared state-of-art methods substantially. Our preliminary MATLAB code will be available at https://github.com/WWLoveTransfer/.