3 papers
cs.DM2025
Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvatures
Abigail Hickok, Andrew J. Blumberg
We study the relationship between discrete analogues of Ricci and scalar curvature that are defined for point clouds and graphs. In the discrete setting, Ricci curvature is replace…
cs.LG2025
EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddings
Tristan Luca Saidi, Abigail Hickok, Bastian Rieck +1
Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations that do not preserve the geometry of noisy and high dimensional data. In particular,…
cs.LG2025
Recovering Manifold Structure Using Ollivier-Ricci Curvature
Tristan Luca Saidi, Abigail Hickok, Andrew J. Blumberg
We introduce ORC-ManL, a new algorithm to prune spurious edges from nearest neighbor graphs using a criterion based on Ollivier-Ricci curvature and estimated metric distortion. Our…