# TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Images

arXiv: https://arxiv.org/abs/2101.08398 · HTML: https://mlsanity.com/paper/2101.08398/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 21 Jan 2021.

## Builds on (most cited first, 10 of 10)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Review of Artificial Intelligence Techniques in Imaging Data Acquisition, Segmentation and Diagnosis for COVID-19](https://mlsanity.com/paper/2004.02731/) (2020)
- [JCS: An Explainable COVID-19 Diagnosis System by Joint Classification and Segmentation](https://mlsanity.com/paper/2004.07054/) (2020)
- [Beyond Deep Residual Learning for Image Restoration: Persistent Homology-Guided Manifold Simplification](https://mlsanity.com/paper/1611.06345/) (2016)
- [Iteratively Pruned Deep Learning Ensembles for COVID-19 Detection in Chest X-rays](https://mlsanity.com/paper/2004.08379/) (2020)
- [Functional Summaries of Persistence Diagrams](https://mlsanity.com/paper/1804.01618/) (2018)
- [Statistical Analysis of Persistence Intensity Functions](https://mlsanity.com/paper/1510.02502/) (2015)
- [Graph Based Analysis for Gene Segment Organization In a Scrambled Genome](https://mlsanity.com/paper/1801.05922/) (2018)

## Built on by (most cited first, 12 of 12)

- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [A persistent homology-based topological loss for CNN-based multi-class segmentation of CMR](https://mlsanity.com/paper/2107.12689/) (2021)
- [Persistent Homology and Graphs Representation Learning](https://mlsanity.com/paper/2102.12926/) (2021)
- [Synthetic Data Generation and Deep Learning for the Topological Analysis of 3D Data](https://mlsanity.com/paper/2309.16968/) (2023)
- [Time-Series Forecasting via Topological Information Supervised Framework with Efficient Topological Feature Learning](https://mlsanity.com/paper/2503.23757/) (2025)
- [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)
- [Statistical and Topological Summaries Aid Disease Detection for Segmented Retinal Vascular Images](https://mlsanity.com/paper/2202.09708/) (2022)
- [Topological structure of complex predictions](https://mlsanity.com/paper/2207.14358/) (2022)
- [Improving Remote Sensing Classification using Topological Data Analysis and Convolutional Neural Networks](https://mlsanity.com/paper/2507.10381/) (2025)
- [Modeling electronic health record data using a knowledge-graph-embedded topic model](https://mlsanity.com/paper/2206.01436/) (2022)
- [LightGBM robust optimization algorithm based on topological data analysis](https://mlsanity.com/paper/2406.13300/) (2024)

## Abstract (arXiv)

Topological Data Analysis (TDA) has emerged recently as a robust tool to extract and compare the structure of datasets. TDA identifies features in data such as connected components and holes and assigns a quantitative measure to these features. Several studies reported that topological features extracted by TDA tools provide unique information about the data, discover new insights, and determine which feature is more related to the outcome. On the other hand, the overwhelming success of deep neural networks in learning patterns and relationships has been proven on a vast array of data applications, images in particular. To capture the characteristics of both powerful tools, we propose textitTDA-Net, a novel ensemble network that fuses topological and deep features for the purpose of enhancing model generalizability and accuracy. We apply the proposed textitTDA-Net to a critical application, which is the automated detection of COVID-19 from CXR images. The experimental results showed that the proposed network achieved excellent performance and suggests the applicability of our method in practice.