Rethink Maximum Mean Discrepancy for Domain Adaptation

Existing domain adaptation methods aim to reduce the distributional difference between the source and target domains and respect their specific discriminative information, by establishing the Maximum Mean Discrepancy (MMD) and the discriminative distances. However, they usually accumulate to consider those statistics and deal with their relationships by estimating parameters blindly. This paper theoretically proves two essential facts: 1) minimizing the MMD equals to maximize the source and target intra-class distances respectively but jointly minimize their variance with some implicit weights, so that the feature discriminability degrades; 2) the relationship between the intra-class and inter-class distances is as one falls, another rises. Based on this, we propose a novel discriminative MMD. On one hand, we consider the intra-class and inter-class distances alone to remove a redundant parameter, and the revealed weights provide their approximate optimal ranges. On the other hand, we design two different strategies to boost the feature discriminability: 1) we directly impose a trade-off parameter on the implicit intra-class distance in MMD to regulate its change; 2) we impose the similar weights revealed in MMD on inter-class distance and maximize it, then a balanced factor could be introduced to quantitatively leverage the relative importance between the feature transferability and its discriminability. The experiments on several benchmark datasets not only prove the validity of theoretical results but also demonstrate that our approach could perform better than the comparative state-of-art methods substantially.