  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.
