Temporal Multiresolution Graph Learning

Estimating time-varying graphs, i.e., a set of graphs in which one graph represents the relationship among nodes in a certain time slot, from observed data is a crucial problem in signal processing, machine learning, and data mining. Although many existing methods only estimate graphs with a single temporal resolution, the actual graphs often demonstrate different relationships in different temporal resolutions. In this study, we propose an approach for time-varying graph learning by leveraging a multiresolution property. The proposed method assumes that time-varying graphs can be decomposed by a linear combination of graphs localized at different temporal resolutions. We formulate a convex optimization problem for temporal multiresolution graph learning. In experiments using synthetic and real data, the proposed method demonstrates the promising objective performances for synthetic data, and obtains reasonable temporal multiresolution graphs from real data.