Researchers have developed a new method called Distance-Matrix Wasserstein (DMW) to more efficiently compare complex data structures like graphs and point clouds. This approach relaxes the computationally intensive Gromov--Wasserstein (GW) distance problem into a hierarchy of Wasserstein statistics that compare laws of random distance matrices. DMW is proven to be a lower bound of GW, with the gap controlled by the sampling error, and offers scalable computation through sliced and multi-scale variations. Experiments show DMW effectively serves as a proxy for structural comparison in various applications. AI
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IMPACT Introduces a more scalable method for comparing complex data structures, potentially improving performance in machine learning tasks involving graph and point cloud analysis.
RANK_REASON Academic paper detailing a new computational method. [lever_c_demoted from research: ic=1 ai=1.0]