# Topological Data Analysis

arXiv: https://arxiv.org/abs/1609.08227 · HTML: https://mlsanity.com/paper/1609.08227/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2016.

## Built on by (most cited first, 16 of 16)

- [Scalable algorithms for physics-informed neural and graph networks](https://mlsanity.com/paper/2205.08332/) (2022)
- [The Topology and Geometry of Neural Representations](https://mlsanity.com/paper/2309.11028/) (2023)
- [Tangent Space and Dimension Estimation with the Wasserstein Distance](https://mlsanity.com/paper/2110.06357/) (2021)
- [Topological Signatures vs. Gradient Histograms: A Comparative Study for Medical Image Classification](https://mlsanity.com/paper/2507.03006/) (2025)
- [Topological Measurement of Deep Neural Networks Using Persistent Homology](https://mlsanity.com/paper/2106.03016/) (2021)
- [Enhancing cluster analysis via topological manifold learning](https://mlsanity.com/paper/2207.00510/) (2022)
- [UDRN: Unified Dimensional Reduction Neural Network for Feature Selection and Feature Projection](https://mlsanity.com/paper/2207.03809/) (2022)
- [Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning](https://mlsanity.com/paper/2408.00220/) (2024)
- [Joint Geometric and Topological Analysis of Hierarchical Datasets](https://mlsanity.com/paper/2104.01395/) (2021)
- [Can Persistent Homology provide an efficient alternative for Evaluation of Knowledge Graph Completion Methods?](https://mlsanity.com/paper/2301.12929/) (2023)
- [Generalized partitioned local depth](https://mlsanity.com/paper/2303.10167/) (2023)
- [Topological data analysis of human vowels: Persistent homologies across representation spaces](https://mlsanity.com/paper/2310.06508/) (2023)
- [Statistical embedding: Beyond principal components](https://mlsanity.com/paper/2106.01858/) (2021)
- [PlasmoData.jl -- A Julia Framework for Modeling and Analyzing Complex Data as Graphs](https://mlsanity.com/paper/2401.11404/) (2024)
- [A cohomology-based Gromov-Hausdorff metric approach for quantifying molecular similarity](https://mlsanity.com/paper/2411.13887/) (2024)
- [Beyond Distance: Quantifying Point Cloud Dynamics with Persistent Homology and Dynamic Optimal Transport](https://mlsanity.com/paper/2603.15683/) (2026)

## Abstract (arXiv)

Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation and persistent homology. This paper reviews some of these methods.