  A common assumption in semi-supervised learning with graph models is that the
class label function varies smoothly on the data graph, resulting in the rather
strict prior that the label function has low-frequency content. Meanwhile, in
many classification problems, the label function may vary abruptly in certain
graph regions, resulting in high-frequency components. Although the
semi-supervised estimation of class labels is an ill-posed problem in general,
in several applications it is possible to find a source graph on which the
label function has similar frequency content to that on the target graph where
the actual classification problem is defined. In this paper, we propose a
method for domain adaptation on graphs motivated by these observations. Our
algorithm is based on learning the spectrum of the label function in a source
graph with many labeled nodes, and transferring the information of the spectrum
to the target graph with fewer labeled nodes. While the frequency content of
the class label function can be identified through the graph Fourier transform,
it is not easy to transfer the Fourier coefficients directly between the two
graphs, since no one-to-one match exists between the Fourier basis vectors of
independently constructed graphs in the domain adaptation setting. We solve
this problem by learning a transformation between the Fourier bases of the two
graphs that flexibly ``aligns'' them. The unknown class label function on the
target graph is then reconstructed such that its spectrum matches that on the
source graph while also ensuring the consistency with the available labels. The
proposed method is tested in the classification of image, online product
review, and social network data sets. Comparative experiments suggest that the
proposed algorithm performs better than recent domain adaptation methods in the
literature in most settings.
