Domain adaption (DA) allows machine learning methods trained on data sampled
from one distribution to be applied to data sampled from another. It is thus of
great practical importance to the application of such methods. Despite the fact
that tensor representations are widely used in Computer Vision to capture
multi-linear relationships that affect the data, most existing DA methods are
applicable to vectors only. This renders them incapable of reflecting and
preserving important structure in many problems. We thus propose here a
learning-based method to adapt the source and target tensor representations
directly, without vectorization. In particular, a set of alignment matrices is
introduced to align the tensor representations from both domains into the
invariant tensor subspace. These alignment matrices and the tensor subspace are
modeled as a joint optimization problem and can be learned adaptively from the
data using the proposed alternative minimization scheme. Extensive experiments
show that our approach is capable of preserving the discriminative power of the
source domain, of resisting the effects of label noise, and works effectively
for small sample sizes, and even one-shot DA. We show that our method
outperforms the state-of-the-art on the task of cross-domain visual recognition
in both efficacy and efficiency, and particularly that it outperforms all
comparators when applied to DA of the convolutional activations of deep
convolutional networks.

提出了一种基于学习的方法，用于直接适应源和目标张量表示，其中引入了一组对准矩阵以将两个领域的张量表示对齐到不变张量子空间，并展示了其在域自适应的卷积激活方面具有最佳性能。