Reproduce “Cluster-Aware Matching via Laplacian Optimal Transport” on OpenResearch
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About this paper
Gabriel Samberg, YoonHaeng Hur, Yuehaw Khoo, Nir Sharon
A new framework, Laplacian Optimal Transport (LapOT) and Refined Simultaneous Clustering (RSC), enables cluster-aware matching and consistent simultaneous clustering of point clouds by integrating structural information into the optimal transport process. It demonstrates improved robustness in 3D shape alignment and consistently aligns intrinsic clusters in high-dimensional financial data.
Key insights
- Laplacian regularization directly encourages the optimal coupling to align points that belong to similar clusters in both point sets, inducing a "cluster-aware" property that is more robust to noise and variations.
- The optimal coupling produced by LapOT naturally tends towards a low-rank structure, which signifies that the matching prioritizes broad, cluster-level correspondences rather than fine-grained point-to-point mappings.
- By conditioning the final clustering on the cluster-aware matching information from LapOT, RSC can overcome the inherent instability of independent clustering algorithms, yielding consistent and meaningful partitions across multiple point clouds.
Summary by alphaXiv.
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