  This paper introduces a new method to solve the cross-domain recognition
problem. Different from the traditional domain adaption methods which rely on a
global domain shift for all classes between source and target domain, the
proposed method is more flexible to capture individual class variations across
domains. By adopting a natural and widely used assumption -- "the data samples
from the same class should lay on a low-dimensional subspace, even if they come
from different domains", the proposed method circumvents the limitation of the
global domain shift, and solves the cross-domain recognition by finding the
compact joint subspaces of source and target domain. Specifically, given
labeled samples in source domain, we construct subspaces for each of the
classes. Then we construct subspaces in the target domain, called anchor
subspaces, by collecting unlabeled samples that are close to each other and
highly likely all fall into the same class. The corresponding class label is
then assigned by minimizing a cost function which reflects the overlap and
topological structure consistency between subspaces across source and target
domains, and within anchor subspaces, respectively.We further combine the
anchor subspaces to corresponding source subspaces to construct the compact
joint subspaces. Subsequently, one-vs-rest SVM classifiers are trained in the
compact joint subspaces and applied to unlabeled data in the target domain. We
evaluate the proposed method on two widely used datasets: object recognition
dataset for computer vision tasks, and sentiment classification dataset for
natural language processing tasks. Comparison results demonstrate that the
proposed method outperforms the comparison methods on both datasets.
