Solving graph compression via optimal transport
This addresses graph compression for machine learning applications, offering a novel method with proven efficiency and performance gains.
The paper tackles graph compression by using optimal transport with prior information, introducing Boolean relaxations and an exact O(d log d) projection algorithm, and shows it outperforms state-of-the-art methods on graph classification tasks.
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for either directed or undirected graphs, and its dual characterization is cast in terms of distributions over the nodes. The compression pertains to the support of node distributions and makes the problem challenging to solve directly. To this end, we introduce Boolean relaxations and specify conditions under which these relaxations are exact. The relaxations admit algorithms with provably fast convergence. Moreover, we provide an exact $O(d \log d)$ algorithm for the subproblem of projecting a $d$-dimensional vector to transformed simplex constraints. Our method outperforms state-of-the-art compression methods on graph classification.