Cluster-Aware Matching via Laplacian Optimal Transport

• URL: http://arxiv.org/abs/2607.16178v1
• Date: Fri, 17 Jul 2026 17:56:51 GMT
• Title: Cluster-Aware Matching via Laplacian Optimal Transport
• Abstract summary: We propose a novel approach for cluster-aware matching based on Laplacian Optimal Transport (LapOT)<n>We show that LapOT indeed produces cluster-aware matching that leads to more consistent and meaningful alignments between point clouds.
• Score: 1.9890930069402575
• License: http://creativecommons.org/licenses/by/4.0/
• 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, we 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. We 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, which can overcome the limitations of independent clustering and yield more stable and interpretable results. We demonstrate the effectiveness of our approach 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.

Related papers

• Counterfactuals for Feature-Weighted Clustering [0.7734726150561086]
  This paper introduces VoICE, a Voronoi-Induced Counterfactual Explainability framework for feature-weighted $k$-means clustering.<n>Rather than treating cluster change as a crossing of a single pairwise centroid boundary, VoICE formulates counterfactual generation as projection onto the full weighted Voronoi region of a target cluster.
  arXiv  Detail & Related papers  (2026-07-16T08:36:04Z)
• A Holistic Method for Superquadric Fitting Using Unsupervised Clustering Analysis [10.759776164959208]
  We present a novel method for fitting superquadrics to point clouds under the contamination of noise and outliers.<n>Our method redefines the problem from a new unsupervised clustering perspective.<n>We provide a theoretical certificate of convergence analysis and demonstrate that the clustering-inspired fitting method can escape local minima.
  arXiv  Detail & Related papers  (2026-05-16T03:20:33Z)
• You Can Trust Your Clustering Model: A Parameter-free Self-Boosting Plug-in for Deep Clustering [73.48306836608124]
  DCBoost is a parameter-free plug-in designed to enhance the global feature structures of current deep clustering models.<n>By harnessing reliable local structural cues, our method aims to elevate clustering performance effectively.
  arXiv  Detail & Related papers  (2025-11-26T09:16:36Z)
• Self-Supervised Graph Embedding Clustering [70.36328717683297]
  K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. We propose a unified framework that integrates manifold learning with K-means, resulting in the self-supervised graph embedding framework.
  arXiv  Detail & Related papers  (2024-09-24T08:59:51Z)
• Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis [28.18800845199871]
  We present a novel non-rigid point set registration method inspired by unsupervised clustering analysis. Our method achieves high accuracy results across various scenarios and surpasses competitors by a significant margin.
  arXiv  Detail & Related papers  (2024-06-27T01:16:44Z)
• Deep Embedding Clustering Driven by Sample Stability [16.53706617383543]
  We propose a deep embedding clustering algorithm driven by sample stability (DECS) Specifically, we start by constructing the initial feature space with an autoencoder and then learn the cluster-oriented embedding feature constrained by sample stability. The experimental results on five datasets illustrate that the proposed method achieves superior performance compared to state-of-the-art clustering approaches.
  arXiv  Detail & Related papers  (2024-01-29T09:19:49Z)
• Point Cloud Classification via Deep Set Linearized Optimal Transport [51.99765487172328]
  We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein space while constructing a classifier to distinguish between various classes of point clouds. We showcase the advantages of our algorithm over the standard deep set approach through experiments on a flow dataset with a limited number of labeled point clouds.
  arXiv  Detail & Related papers  (2024-01-02T23:26:33Z)
• Local Sample-weighted Multiple Kernel Clustering with Consensus Discriminative Graph [73.68184322526338]
  Multiple kernel clustering (MKC) is committed to achieving optimal information fusion from a set of base kernels. This paper proposes a novel local sample-weighted multiple kernel clustering model. Experimental results demonstrate that our LSWMKC possesses better local manifold representation and outperforms existing kernel or graph-based clustering algo-rithms.
  arXiv  Detail & Related papers  (2022-07-05T05:00:38Z)
• Perfect Spectral Clustering with Discrete Covariates [68.8204255655161]
  We propose a spectral algorithm that achieves perfect clustering with high probability on a class of large, sparse networks. Our method is the first to offer a guarantee of consistent latent structure recovery using spectral clustering.
  arXiv  Detail & Related papers  (2022-05-17T01:41:06Z)
• Gradient Based Clustering [72.15857783681658]
  We propose a general approach for distance based clustering, using the gradient of the cost function that measures clustering quality. The approach is an iterative two step procedure (alternating between cluster assignment and cluster center updates) and is applicable to a wide range of functions.
  arXiv  Detail & Related papers  (2022-02-01T19:31:15Z)
• Shift of Pairwise Similarities for Data Clustering [3.3178024597495903]
  We consider the case where the regularization term is the sum of the squared size of the clusters, and then generalize it to adaptive regularization of the pairwise similarities.<n>This leads to shifting (adaptively) the pairwise similarities which might make some of them negative.<n>We then propose an efficient local search optimization algorithm with fast theoretical convergence rate to solve the new clustering problem.
  arXiv  Detail & Related papers  (2021-10-25T16:55:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.