Domain Adaptation on Graphs by Learning Aligned Graph Bases

We propose a method for domain adaptation on graphs. Given sufficiently many observations of the label function on a source graph, we study the problem of transferring the label information from the source graph to a target graph for estimating the target label function. Our assumption about the relation between the two domains is that the frequency content of the label function, regarded as a graph signal, has similar characteristics over the source and the target graphs. We propose a method to learn a pair of coherent bases on the two graphs, such that the corresponding source and target graph basis vectors have similar spectral content, while "aligning" the two graphs at the same time so that the reconstructed source and target label functions have similar coefficients over the bases. Experiments on several types of data sets suggest that the proposed method compares quite favorably to reference domain adaptation methods. To the best of our knowledge, our treatment is the first to study the domain adaptation problem in a purely graph-based setting with no need for embedding the data in an ambient space. This feature is particularly convenient for many problems of interest concerning learning on graphs or networks.