Cluster-Aware Matching via Laplacian Optimal Transport

2026-07-20 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

Researchers Gabriel Samberg, YoonHaeng Hur, Yuehaw Khoo, and Nir Sharon introduce Laplacian Optimal Transport (LapOT), a novel method for cluster-aware matching of point clouds. Unlike traditional point-to-point correspondence, LapOT focuses on robust region-to-region alignment by regularizing the optimal transport problem with quadratic Laplacian terms derived from similarity graphs. This encourages the optimal coupling to respect the intrinsic cluster structure of both point sets. They also propose Refined Simultaneous Clustering (RSC), a complementary technique that leverages LapOT's cluster-aware coupling to generate consistent partitions across point sets, overcoming the instability of independent clustering. Theoretical analysis and empirical experiments, including applications to 3D shapes from the CAPOD dataset and stock market data (S&P 500, Japanese stocks), demonstrate LapOT's effectiveness in producing more consistent and meaningful alignments.

Key takeaway

For Machine Learning Engineers working with point cloud data that exhibits intrinsic cluster structures, LapOT offers a robust alternative to traditional point-to-point matching. You should consider integrating Laplacian regularization into your optimal transport pipelines to achieve more stable and interpretable region-to-region alignments, especially when independent clustering proves inconsistent. Explore its application for simultaneous clustering to improve partition consistency.

Key insights

Laplacian Optimal Transport (LapOT) enables robust, cluster-aware point cloud matching by integrating graph-based regularization.

Principles

• Optimal coupling should respect intrinsic cluster structure.
• Stronger Laplacian regularization yields pronounced low-rank coupling.
• Matching and clustering are coupled problems.

Method

LapOT regularizes optimal transport with quadratic Laplacian terms from similarity graphs. Refined Simultaneous Clustering (RSC) then uses this cluster-aware coupling to produce consistent partitions.

In practice

• Aligning 3D shapes (e.g., human figures).
• Analyzing stock market data for cluster structure.

Topics

• Optimal Transport
• Point Cloud Matching
• Graph Laplacian
• Cluster Analysis
• Refined Simultaneous Clustering
• Low-Rank Approximation

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.