mlsanityData to 7 Oct 2026

Subsampling Methods for Persistent Homology

arXiv 1406.1901 ↗First posted 7 Jun 2014math.AT cs.CG stat.APcited by 17

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Abstract (arXiv)

Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the persistent homology is prohibitive due to the combinatorial nature of the existing algorithms. We propose to compute the persistent homology of several subsamples of the data and then combine the resulting estimates. We study the risk of two estimators and we prove that the subsampling approach carries stable topological information while achieving a great reduction in computational complexity.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Jun 2014.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 2; 2023: 4; 2024: 3; 2025: 3; 2026: 2.

17 papers.

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  1. 2021From Geometry to Topology: Inverse Theorems for Distributed Persistencecited by 10
  2. 2023Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphscited by 9
  3. 2021Cycle Registration in Persistent Homology with Applications in Topological Bootstrapcited by 8
  4. 2022Approximating Persistent Homology for Large Datasetscited by 8
  5. 2024Diffeomorphic interpolation for efficient persistence-based topological optimizationcited by 6
  6. 2024Mapping the Multiverse of Latent Representationscited by 5
  7. 2025The Flood Complex: Large-Scale Persistent Homology on Millions of Pointscited by 5
  8. 2025The Shape of Adversarial Influence: Characterizing LLM Latent Spaces with Persistent Homologycited by 4
  9. 2022Time-inhomogeneous diffusion geometry and topologycited by 3
  10. 2023Persistent Homology for High-dimensional Data Based on Spectral Methodscited by 3
  11. 2021Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measurescited by 2
  12. 2023Topology Estimation of Simulated 4D Image Data by Combining Downscaling and Convolutional Neural Networkscited by 2
5 more
  1. 2025Towards Scalable Topological Regularizerscited by 1
  2. 2023A stability theorem for bigraded persistence barcodescited by 0
  3. 2024Neural Persistence Dynamicscited by 0
  4. 2026FILTR: Extracting Topological Features from Pretrained 3D Modelscited by 0
  5. 2026Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagramscited by 0