SEINT proposes a training-free SE(p)-invariant metric for structural data like 3D point clouds and molecules. It compresses high-dimensional distributions into 1D isometric representations (PTD/DcPTD) for fast 1D Optimal Transport computation. Achieves strict metric properties with near-linear complexity.
Key Points
- 1.Training-free 1D representations PTD/DcPTD for SE(p)-invariant mapping
- 2.SEINT distance via 1D OT, proven metric on norm spaces
- 3.Near-linear O(N log N) complexity for common norms
- 4.Applies to 3D point clouds, molecular configs without alignment
Impact Analysis
Enables scalable, theoretically robust distance metrics for 3D/ML tasks, outperforming alignment-heavy methods in speed and guarantees.
Technical Details
Constructs equivariant 1D histograms from radial/diffeomorphic projections; 1D OT yields isometric embedding preserving rigid invariance.
