# Subsampling Methods for Persistent Homology

arXiv: https://arxiv.org/abs/1406.1901 · HTML: https://mlsanity.com/paper/1406.1901/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2014.

## Built on by (most cited first, 17 of 17)

- [From Geometry to Topology: Inverse Theorems for Distributed Persistence](https://mlsanity.com/paper/2101.12288/) (2021)
- [Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphs](https://mlsanity.com/paper/2304.11140/) (2023)
- [Cycle Registration in Persistent Homology with Applications in Topological Bootstrap](https://mlsanity.com/paper/2101.00698/) (2021)
- [Approximating Persistent Homology for Large Datasets](https://mlsanity.com/paper/2204.09155/) (2022)
- [Diffeomorphic interpolation for efficient persistence-based topological optimization](https://mlsanity.com/paper/2405.18820/) (2024)
- [The Flood Complex: Large-Scale Persistent Homology on Millions of Points](https://mlsanity.com/paper/2509.22432/) (2025)
- [Mapping the Multiverse of Latent Representations](https://mlsanity.com/paper/2402.01514/) (2024)
- [The Shape of Adversarial Influence: Characterizing LLM Latent Spaces with Persistent Homology](https://mlsanity.com/paper/2505.20435/) (2025)
- [Time-inhomogeneous diffusion geometry and topology](https://mlsanity.com/paper/2203.14860/) (2022)
- [Persistent Homology for High-dimensional Data Based on Spectral Methods](https://mlsanity.com/paper/2311.03087/) (2023)
- [Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures](https://mlsanity.com/paper/2104.01672/) (2021)
- [Topology Estimation of Simulated 4D Image Data by Combining Downscaling and Convolutional Neural Networks](https://mlsanity.com/paper/2306.14442/) (2023)
- [Towards Scalable Topological Regularizers](https://mlsanity.com/paper/2501.14641/) (2025)
- [A stability theorem for bigraded persistence barcodes](https://mlsanity.com/paper/2303.14694/) (2023)
- [Neural Persistence Dynamics](https://mlsanity.com/paper/2405.15732/) (2024)
- [FILTR: Extracting Topological Features from Pretrained 3D Models](https://mlsanity.com/paper/2604.22334/) (2026)
- [Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams](https://mlsanity.com/paper/2607.27126/) (2026)

## 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.