Research map / Learning theory and algorithms / Optimal transport
Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the Sinkhorn OT method instead of Hera for persistence-diagram distance estimation | Persistence-diagram distance estimation · Random diagram pairs with 10 to 5000 points | runtime scaling | Helped |
| Use the Sinkhorn barycenter algorithm instead of B-Munkres | Persistence-diagram barycenter estimation · 10 diagrams with n to 2n points, n from 1 to 500 | runtime | Helped |
| Use the convex Eulerian Sinkhorn approach rather than B-Munkres initialization | Persistence-diagram barycenter estimation · Toy set of 3 diagrams | energy | Helped |
| Use the convex Eulerian Sinkhorn approach rather than the arithmetic mean | Persistence-diagram barycenter estimation · Toy set of 3 diagrams | energy: 0.72 | Helped |
| Apply the C-transform to the Sinkhorn dual iterate (ablation) | Sinkhorn distance approximation · 100 random diagram pairs, 100 × 100 grid | lower-bound quality | Helped |
| Decrease the entropic regularization parameter γ (ablation) | Sinkhorn barycenter estimation · Three persistence diagrams | energy | Helped |
| Initialize B-Munkres from different input diagrams (ablation) | B-Munkres barycenter algorithm · Toy set of 3 diagrams | energy | Mixed |
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- Transport Clustering: Solving Low-Rank Optimal Transport via Clustering (ICML 2026 · similarity 0.88)
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- Computing Optimal Transport Maps and Wasserstein Barycenters Using Conditional Normalizing Flows (ICML 2025 · similarity 0.85)
- Wasserstein convergence of Cech persistence diagrams for samplings of submanifolds (NeurIPS 2024 · similarity 0.84)
- Hierarchical Refinement: Optimal Transport to Infinity and Beyond (ICML 2025 · similarity 0.84)
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