mlsanityData to 7 Oct 2026

Point-Level Topological Representation Learning on Point Clouds

arXiv 2406.02300 ↗First posted 4 Jun 2024math.AT cs.CG cs.LGcited by 4

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Abstract (arXiv)

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description of the global structure of the point cloud. However, common machine learning applications like classification require point-level information and features to be available. In this paper, we bridge this gap and propose a novel method to extract node-level topological features from complex point clouds using discrete variants of concepts from algebraic topology and differential geometry. We verify the effectiveness of these topological point features (TOPF) on both synthetic and real-world data and study their robustness under noise and heterogeneous sampling.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 25 of its 80 references that are in the map. First posted on arXiv 4 Jun 2024.

Builds on

25 of 80 references.

References · 25

  1. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  2. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  3. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,841
  4. 2016node2vec: Scalable Feature Learning for Networkscited by 1,913
  5. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 235
  6. 2017An introduction to Topological Data Analysis: fundamental and practical aspects for data scientistscited by 171
  7. 2019Topological Autoencoderscited by 124
  8. 2019Ripser: efficient computation of Vietoris-Rips persistence barcodescited by 115
  9. 2018Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplaciancited by 84
  10. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 81
  11. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  12. 2020Persistent Laplacians: properties, algorithms and implicationscited by 28
13 more
  1. 2023GRIL: A 2-parameter Persistence Based Vectorization for Machine Learningcited by 13
  2. 2021The decomposition of the higher-order homology embedding constructed from the k-Laplaciancited by 8
  3. 2019A Notion of Harmonic Clustering in Simplicial Complexescited by 7
  4. 2021Helmholtzian Eigenmap: Topological feature discovery & edge flow learning from point cloud datacited by 7
  5. 2021WSDesc: Weakly Supervised 3D Local Descriptor Learning for Point Cloud Registrationcited by 7
  6. 2018Sparse Circular Coordinates via Principal mathbbZ-Bundlescited by 6
  7. 2024Graphcode: Learning from multiparameter persistent homology using graph neural networkscited by 6
  8. 2024Diffeomorphic interpolation for efficient persistence-based topological optimizationcited by 6
  9. 2023Topological Point Cloud Clusteringcited by 5
  10. 2023Topological Node2vec: Enhanced Graph Embedding via Persistent Homologycited by 5
  11. 2023Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PHcited by 3
  12. 2023Circular Coordinates for Density-Robust Analysiscited by 2
  13. 2024Novel definition and quantitative analysis of branch structure with topological data analysiscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 1.

4 papers.

  1. 2024Topological Trajectory Classification and Landmark Inference on Simplicial Complexescited by 1
  2. 2025On the Sheafification of Higher-Order Message Passingcited by 1
  3. 2025Efficient Sparsification of Simplicial Complexes via Local Densities of Statescited by 0
  4. 2026Selecting Interpretable Circular Coordinates from Datacited by 0