Multiview Graph Learning Based on Node Perturbation Model

Graph topology inference, i.e., learning graphs from a given set of nodal observations, is a significant task in many application domains. Existing approaches are mostly limited to learning a single graph assuming that the observed data is homogeneous. This is problematic because many modern datasets are heterogeneous or mixed and involve multiple related graphs, i.e., multiview graphs. Recent work proposing to learn multiview graphs ensures the similarity of learned view graphs through either pairwise regularization or consensus-based regularization. In most of the existing approaches, the similarities and differences between networks are assumed to be driven by individual edges. However, a node-based approach provides a more intuitive interpretation of the network differences. In this paper, we introduce a node perturbation model to learn multiview graph Laplacians with the assumption that the differences between the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> networks are due to individual nodes that are perturbed across views. An optimization framework is formulated to simultaneously learn the graph Laplacians of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> views with the assumption that the observed signals are smooth with respect to the underlying graph Laplacians. The proposed method is compared to existing edge-based multiview Laplacian learning methods as well as joint graphical Lasso based structure inference methods.