  Domain adaptation (DA) aims to generalize a learning model across training
and testing data despite the mismatch of their data distributions. In light of
a theoretical estimation of upper error bound, we argue in this paper that an
effective DA method should 1) search a shared feature subspace where source and
target data are not only aligned in terms of distributions as most state of the
art DA methods do, but also discriminative in that instances of different
classes are well separated; 2) account for the geometric structure of the
underlying data manifold when inferring data labels on the target domain. In
comparison with a baseline DA method which only cares about data distribution
alignment between source and target, we derive three different DA models,
namely CDDA, GA-DA, and DGA-DA, to highlight the contribution of Close yet
Discriminative DA(CDDA) based on 1), Geometry Aware DA (GA-DA) based on 2), and
finally Discriminative and Geometry Aware DA (DGA-DA) implementing jointly 1)
and 2). Using both synthetic and real data, we show the effectiveness of the
proposed approach which consistently outperforms state of the art DA methods
over 36 image classification DA tasks through 6 popular benchmarks. We further
carry out in-depth analysis of the proposed DA method in quantifying the
contribution of each term of our DA model and provide insights into the
proposed DA methods in visualizing both real and synthetic data.
