# A Topological "Reading" Lesson: Classification of MNIST using TDA

arXiv: https://arxiv.org/abs/1910.08345 · HTML: https://mlsanity.com/paper/1910.08345/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2019.

## Built on by (most cited first, 21 of 21)

- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [Persistent Homology with Improved Locality Information for more Effective Delineation](https://mlsanity.com/paper/2110.06295/) (2021)
- [Persistent Homology for Breast Tumor Classification using Mammogram Scans](https://mlsanity.com/paper/2201.02295/) (2022)
- [Landslide Topology Uncovers Failure Movements](https://mlsanity.com/paper/2310.09631/) (2023)
- [A Multi-parameter Persistence Framework for Mathematical Morphology](https://mlsanity.com/paper/2103.13013/) (2021)
- [Image Classification using Combination of Topological Features and Neural Networks](https://mlsanity.com/paper/2311.06375/) (2023)
- [TACO-Net: Topological Signatures Triumph in 3D Object Classification](https://mlsanity.com/paper/2509.24802/) (2025)
- [A Topological Machine Learning Pipeline for Classification](https://mlsanity.com/paper/2309.15276/) (2023)
- [GeoTop: Advancing Image Classification with Geometric-Topological Analysis](https://mlsanity.com/paper/2311.16157/) (2023)
- [Comparing the Effects of Persistence Barcodes Aggregation and Feature Concatenation on Medical Imaging](https://mlsanity.com/paper/2505.23637/) (2025)
- [Improving Remote Sensing Classification using Topological Data Analysis and Convolutional Neural Networks](https://mlsanity.com/paper/2507.10381/) (2025)
- [CuMPerLay: Learning Cubical Multiparameter Persistence Vectorizations](https://mlsanity.com/paper/2510.12795/) (2025)
- [Multi-dimensional Persistent Sheaf Laplacians for Image Analysis](https://mlsanity.com/paper/2602.14846/) (2026)
- [Image recognition via Vietoris-Rips complex](https://mlsanity.com/paper/2109.02231/) (2021)
- [Topological Data Analysis (TDA) Techniques Enhance Hand Pose Classification from ECoG Neural Recordings](https://mlsanity.com/paper/2110.04653/) (2021)
- [Using Topological Data Analysis to classify Encrypted Bits](https://mlsanity.com/paper/2301.07393/) (2023)
- [A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams](https://mlsanity.com/paper/2402.14489/) (2024)
- [Standardness Clouds Meaning: A Position Regarding the Informed Usage of Standard Datasets](https://mlsanity.com/paper/2406.13552/) (2024)
- [Persistence kernels for classification: A comparative study](https://mlsanity.com/paper/2408.07090/) (2024)
- [A Novel Patch-Based TDA Approach for Computed Tomography Imaging](https://mlsanity.com/paper/2512.12108/) (2025)
- [Recovering topological information of light by topological learning](https://mlsanity.com/paper/2609.06542/) (2026)

## Abstract (arXiv)

We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural grayscale filtration, and different filtrations defined on the binarized image. We show that this topological machine learning pipeline can be used as a highly relevant dimensionality reduction by applying it to the MNIST digits dataset. We conduct a feature selection and study their correlations while providing an intuitive interpretation of their importance, which is relevant in both machine learning and TDA. Finally, we show that we can classify digit images while reducing the size of the feature set by a factor 5 compared to the grayscale pixel value features and maintain similar accuracy.