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 \textit{TDA-Net}, a novel ensemble network that fuses topological and deep features for the purpose of enhancing model generalizability and accuracy. We apply the proposed \textit{TDA-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.

中文翻译：

---

TDA-Net：融合永久性同源性和深度学习功能的胸部X射线图像中的COVID-19检测

拓扑数据分析（TDA）最近成为一种强大的工具，可以提取和比较数据集的结构。TDA会识别数据中的特征（例如连接的零件和孔），并为这些特征分配定量度量。几项研究报告说，TDA工具提取的拓扑特征可提供有关数据的独特信息，发现新见解并确定哪个特征与结果更相关。另一方面，深层神经网络在学习模式和关系方面取得了压倒性的成功，这已经在大量的数据应用程序中得到了证明，尤其是图像。为了捕获这两种强大工具的特性，我们提出了\ textit {TDA-Net}，这是一种新颖的集成网络，融合了拓扑和深层功能，以增强模型的通用性和准确性。我们将建议的\ textit {TDA-Net}应用到关键应用程序，即从CXR图像自动检测COVID-19。实验结果表明，所提出的网络具有良好的性能，表明了该方法在实践中的适用性。