Graph Domain Adaptation with Localized Graph Signal Representations

Graph Domain Adaptation with Localized Graph Signal Representations Yusuf Yi git Pilavcı, Eylem Tu g ce G uneyi, Cemil Cengiz and Elif Vural Abstract In this paper we propose a domain adaptation algorithm designed for graph domains. Given a source graph with many labeled nodes and a target graph with few or no labeled nodes, we aim to estimate the target labels by making use of the similarity between the characteristics of the variation of the label functions on the two graphs. Our assumption about the source and the target domains is that the local behaviour of the label function, such as its spread and speed of variation on the graph, bears resemblance between the two graphs. We estimate the unknown target labels by solving an optimization problem where the label information is transferred from the source graph to the target graph based on the prior that the projections of the label functions onto localized graph bases be similar between the source and the target graphs. In order to efficiently capture the local variation of the label functions on the graphs, spectral graph wavelets are used as the graph bases. Experimentation on various data sets shows that the proposed method yields quite satisfactory classification accuracy compared to reference domain adaptation methods. Keywords: Domain adaptation, spectral graph theory, graph signal processing, spectral graph wavelets, graph Laplacian 1 Introduction A common assumption in machine learning is that the training and the test data are sampled from the same distribution. Domain adaptation methods aim to provide solutions to machine learning problems by dealing with this distribution discrepancy. In domain adaptation, a source domain and a target domain are considered where the label information is mostly available for the data samples in the source domain, and few or none of the class labels are known in the target domain. The purpose is then to improve the learning performance in the target domain by making use Y. Y. Pilavcı is with the GIPSA Lab at Universit e Grenoble Alpes, Grenoble. C. Cengiz is with the Dept. of Computer Science and Engineering at Ko c University, Istanbul. Most part of this work was performed while the authors were at METU. 1 arXiv:1911.02883v1 A variety of approaches have been proposed so far for the domain adaptation problem. Some methods are based on reweighing the samples for removing the sample selection bias [1, 2]. Another common solution is to align the source and the target domains through feature space mappings.