Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms
The paper extends quantization from clustering points to clustering the geometry those points live in.
Beier and Eckstein study Gromov-Wasserstein quantization, where the approximation target includes ambient structure rather than only locations in a fixed space. They prove solutions exist and give a characterization supporting a Lloyd-style algorithm. The paper also computes rates for common Euclidean geometries and compares them with standard Wasserstein quantization. Experiments cover 3D shape geodesics and structured neural-network pruning, with approximation quality often matching the predicted rates. ArXiv · AI/CL/LG's note
Beier and Eckstein study Gromov-Wasserstein quantization, where the approximation target includes ambient structure rather than only locations in a fixed space. They prove solutions exist and give a characterization supporting a Lloyd-style algorithm. The paper also computes rates for common Euclidean geometries and compares them with standard Wasserstein quantization. Experiments cover 3D shape geodesics and structured neural-network pruning, with approximation quality often matching the predicted rates. ArXiv · AI/CL/LG's note
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