  Visual domain adaptation aims to learn robust classifiers for the target
domain by leveraging knowledge from a source domain. Existing methods either
attempt to align the cross-domain distributions, or perform manifold subspace
learning. However, there are two significant challenges: (1) degenerated
feature transformation, which means that distribution alignment is often
performed in the original feature space, where feature distortions are hard to
overcome. On the other hand, subspace learning is not sufficient to reduce the
distribution divergence. (2) unevaluated distribution alignment, which means
that existing distribution alignment methods only align the marginal and
conditional distributions with equal importance, while they fail to evaluate
the different importance of these two distributions in real applications. In
this paper, we propose a Manifold Embedded Distribution Alignment (MEDA)
approach to address these challenges. MEDA learns a domain-invariant classifier
in Grassmann manifold with structural risk minimization, while performing
dynamic distribution alignment to quantitatively account for the relative
importance of marginal and conditional distributions. To the best of our
knowledge, MEDA is the first attempt to perform dynamic distribution alignment
for manifold domain adaptation. Extensive experiments demonstrate that MEDA
shows significant improvements in classification accuracy compared to
state-of-the-art traditional and deep methods.
