This paper introduces Gromov-Wasserstein (GW) quantization as an extension of traditional k-means clustering. Unlike standard Wasserstein quantization which clusters points within a space, GW quantization also considers the geometry of the space itself. The research proves the existence of solutions for GW quantization and proposes an algorithm analogous to Lloyd's algorithm for numerical approximation. The study also analyzes quantization rates for Euclidean geometries and demonstrates through experiments that GW quantization offers new modeling capabilities, such as for 3D shapes and neural network pruning. AI
RANK_REASON The item is a research paper detailing a new algorithm and its applications. [lever_c_demoted from research: ic=1 ai=1.0]
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- 3d Shapes
- Euclidean geometries
- Gromov--Wasserstein
- k-means clustering
- Lloyd's algorithm
- Neural Networks
- Wasserstein metric
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