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

Abstract

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 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 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.

Persistent Homology and Graphs Representation Learning

“…Recently, there has been multiple efforts to provide a partial answer for the above question. For example, several studies Nielson et al (2015); Joshi & Joshi (2019) reported that the topological features extracted by the persistence diagram can 1) track different information from the original encodings obtained from the raw data Dey et al (2017); Hajij et al (2021) and 2) determine which predictors are more related to the outcome. In addition, the topological analysis of a graph allows to extract features that are invariant to the spatial transformation and more robust to noise Zheng (2015); Bae et al (2017).…”

“…In addition, the fact that persistence homology tracks different information from the original deep learning-based representations (Dey et al (2017); Hajij et al (2021)) suggests that combining the encodings obtained from a persistent homology and other invariants obtained directly from node embedding should increase the quality of the learning task at hand. Further, persistent homology provides a clear, concise and rigorous method to quantify the level of expressiveness of the embeddings as we shall see in Section 5.…”

Using Persistence Barcode to Show the Impact of Data Complexity on the Neural Network Architecture

“…The persistent homology is computed as on the simplicial complex. Furthermore, the final result can be stored in various visualization structures such as a multi-set structure called persistence diagram or in persistence barcode [32]. The barcode indicates the topological features that are computed from a simplicial complex [33].…”