Learning the Geometry of Data: A Mathematical Review of Shape Space Analysis
Gary P. T. Choi, Khanh Dao Duc, Shira Faigenbaum-Golovin, Karen Habermann, Emmanuel Hartman, Christoph von Tycowicz, Chi Zhang, Wenjun Zhao, Felix Zhou
math.ST, cs.LG, stat.ML
Submitted: 2026-06-15
Comments: 79 pages, 10 figures, 8 tables
Code: https://github.com/pyg-team/pytorch_geometric
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- Simulating conditioned diffusions on manifolds
- Transformed Multi-view 3D Shape Features with Contrastive Learning
- SOM-VAE: Interpretable Discrete Representation Learning on Time Series
- Score matching for sub-Riemannian bridge sampling
- Most probable paths for developed processes
- Stochastic completeness for landmark space
- Topological Deep Learning: Going Beyond Graph Data
- Self Supervised Networks for Learning Latent Space Representations of Human Body Scans and Motions
- Robust Watertight Manifold Surface Generation Method for ShapeNet Models
- A Lower Bound for Estimating Fr'echet Means
- Simulation of Conditioned Semimartingales on Riemannian Manifolds
- Riemannian Center of Mass and so called karcher mean
- Adversarial Autoencoders
- A central limit theorem for random tangent fields on stratified spaces
- Central limit theorems for Fr'echet means on stratified spaces
- Geometry of measures on smoothly stratified metric spaces
- Shadow geometry at singular points of CAT(k) spaces
- Deep Level Sets: Implicit Surface Representations for 3D Shape Inference
- Introduction to the Bag of Features Paradigm for Image Classification and Retrieval
- En masse scanning and automated surfacing of small objects using Micro-CT
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