# Image Classification using Combination of Topological Features and Neural Networks

arXiv: https://arxiv.org/abs/2311.06375 · HTML: https://mlsanity.com/paper/2311.06375/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 10 Nov 2023.

## Builds on (most cited first, 11 of 11)

- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [A Topological "Reading" Lesson: Classification of MNIST using TDA](https://mlsanity.com/paper/1910.08345/) (2019)
- [TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Images](https://mlsanity.com/paper/2101.08398/) (2021)
- [Topological Machine Learning with Persistence Indicator Functions](https://mlsanity.com/paper/1907.13496/) (2019)
- [Topological Analysis of Syntactic Structures](https://mlsanity.com/paper/1903.05181/) (2019)
- [Data-driven and Automatic Surface Texture Analysis Using Persistent Homology](https://mlsanity.com/paper/2110.10005/) (2021)
- [Learning quantum phase transitions through Topological Data Analysis](https://mlsanity.com/paper/2109.09555/) (2021)
- [A Topological Machine Learning Pipeline for Classification](https://mlsanity.com/paper/2309.15276/) (2023)

## Built on by (most cited first, 2 of 2)

- [HaSPeR: An Image Repository for Hand Shadow Puppet Recognition](https://mlsanity.com/paper/2408.10360/) (2024)
- [Topology-Informed Neural Networks for Flood Detection in Optical and Synthetic Aperture Radar Imagery](https://mlsanity.com/paper/2606.26204/) (2026)

## Abstract (arXiv)

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA, the concepts of complexes and filtration are building blocks. Firstly, a filtration is constructed from some complex. Then, persistent homology classes are computed, and their evolution along the filtration is visualized through the persistence diagram. Additionally, we applied vectorization techniques to the persistence diagram to make this topological information compatible with machine learning algorithms. This was carried out with the aim of classifying images from multiple classes in the MNIST dataset. Our approach inserts topological features into deep learning approaches composed by single and two-streams neural networks architectures based on a multi-layer perceptron (MLP) and a convolutional neral network (CNN) taylored for multi-class classification in the MNIST dataset. In our analysis, we evaluated the obtained results and compared them with the outcomes achieved through the baselines that are available in the TensorFlow library. The main conclusion is that topological information may increase neural network accuracy in multi-class classification tasks with the price of computational complexity of persistent homology calculation. Up to the best of our knowledge, it is the first work that combines deep learning features and the combination of topological features for multi-class classification tasks.