Paper Overview
- Research areas: stat.ML, cs.LG, math.NA
- Authors: Gabriel Samberg, YoonHaeng Hur, Yuehaw Khoo
- Published: 2026-07-21
- arXiv: 2507.15485
- LapOT: optimal transport regularized with quadratic Laplacian terms from point cloud similarity graphs, producing cluster-aware couplings
- RSC: refined simultaneous clustering that yields consistent partitions across point sets using the LapOT coupling
- Theoretical analysis and empirical validation showing more robust region-to-region alignment than point-to-point matching
Abstract
In many applications of matching, the point clouds to be matched are not merely unstructured sets of points but rather samples from distributions with an intrinsic cluster structure. In such cases, as individual points are often interchangeable within a coherent region, finding a robust region-to-region alignment is more desirable than establishing a precise point-to-point correspondence.
To this end, the authors propose a novel approach for cluster-aware matching based on Laplacian Optimal Transport (LapOT). The key idea is to regularize the optimal transport problem with quadratic Laplacian terms constructed from similarity graphs of the point clouds, which encourages the optimal coupling to respect the cluster structure of both point sets.
They also introduce Refined Simultaneous Clustering (RSC), a method that leverages the cluster-aware coupling obtained from LapOT to produce consistent partitions across the point sets. RSC can overcome the limitations of independent clustering and yields more stable and interpretable results.
The effectiveness of the approach is demonstrated through theoretical analysis and empirical experiments, showing that LapOT indeed produces cluster-aware matching that leads to more consistent and meaningful alignments between point clouds.
Key Contributions
*Auto-collected on 2026-07-21*