mlsanityData to 7 Oct 2026

Topological Point Cloud Clustering

arXiv 2303.16716 ↗First posted 29 Mar 2023math.AT cs.CG cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and topological data analysis and is based on considering the spectral properties of a simplicial complex associated to the considered point cloud. As it is based on considering sparse eigenvector computations, TPCC is similarly easy to interpret and implement as spectral clustering. However, by focusing not just on a single matrix associated to a graph created from the point cloud data, but on a whole set of Hodge-Laplacians associated to an appropriately constructed simplicial complex, we can leverage a far richer set of topological features to characterize the data points within the point cloud and benefit from the relative robustness of topological techniques against noise. We test the performance of TPCC on both synthetic and real-world data and compare it with classical spectral clustering.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 16 of its 57 references that are in the map. First posted on arXiv 29 Mar 2023.

Builds on

16 of 57 references.

References · 16

  1. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  2. 2020Simplicial Neural Networkscited by 105
  3. 2018Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplaciancited by 84
  4. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 81
  5. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  6. 2018DTM-based Filtrationscited by 16
  7. 2021Dist2Cycle: A Simplicial Neural Network for Homology Localizationcited by 16
  8. 2014Using persistent homology and dynamical distances to analyze protein bindingcited by 15
  9. 2017Volume Optimal Cycle: Tightest representative cycle of a generator on persistent homologycited by 12
  10. 2021The decomposition of the higher-order homology embedding constructed from the k-Laplaciancited by 8
  11. 2019A Notion of Harmonic Clustering in Simplicial Complexescited by 7
  12. 2021Spectral Detection of Simplicial Communities via Hodge Laplacianscited by 7
4 more
  1. 2018Sparse Circular Coordinates via Principal mathbbZ-Bundlescited by 6
  2. 2021Go with the Flow? A Large-Scale Analysis of Health Care Delivery Networks in the United States Using Hodge Theorycited by 5
  3. 2021Outlier Detection for Trajectories via Flow-embeddingscited by 4
  4. 2019Recovering the homology of immersed manifoldscited by 3

Built on by

Cited by year

Citing papers per year: 2023: 2; 2024: 2; 2025: 1.

5 papers.

  1. 2023Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equalcited by 5
  2. 2023Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structurescited by 4
  3. 2024Point-Level Topological Representation Learning on Point Cloudscited by 4
  4. 2024A Spectral Framework for Tracking Communities in Evolving Networkscited by 0
  5. 2025Topology-Driven Clustering: Enhancing Performance with Betti Number Filtrationcited by 0