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Hierarchical abstractions are a methodology for solving large-scale graphproblems in various disciplines. Coarsening is one such approach: it generatesa pyramid of graphs whereby the one in the next level is a structural summaryof the prior one. With a long history in scientific computing, many coarseningstrategies were developed based on mathematically driven heuristics. Recently,resurgent interests exist in deep learning to design hierarchical methodslearnable through differentiable parameterization. These approaches are pairedwith downstream tasks for supervised learning. In practice, however, supervisedsignals (e.g., labels) are scarce and are often laborious to obtain. In thiswork, we propose an unsupervised approach, coined OTCoarsening, with the use ofoptimal transport. Both the coarsening matrix and the transport cost matrix areparameterized, so that an optimal coarsening strategy can be learned andtailored for a given set of graphs. We demonstrate that the proposed approachproduces meaningful coarse graphs and yields competitive performance comparedwith supervised methods for graph classification and regression.

Unsupervised Learning of Graph Hierarchical Abstractions with Differentiable Coarsening and Optimal Transport