Topological data analysis and machine learning for COVID-19 detection in CT scan lung images

Abstract

COVID-19 has claimed the lives of thousands over the past years. Although pathogenic laboratory testing is the established standard, it carries a significant drawback with a notable rate of false negatives. Consequently, there is an urgent need for alternative diagnostic approaches to combat this threat. In response to this pressing need for accurate and parameter-free methods for COVID-19 identification, particularly within lung images, we introduce a novel approach that combines the principles of topological data analysis with the capabilities of machine learning. Our proposed methodology entails the extraction of persistent homology features from lung images, effectively capturing the intrinsic topological properties inherent in the data. These extracted persistent homology features then serve as inputs for various machine learning methods employed for classification purposes. Our primary objective is to achieve exceptional accuracy in the detection of COVID-19 all while showcasing the effectiveness of these topological features. The experimental results demonstrate that the Random Forest Classifier and the Support Vector Machine models outperform the rest, showcasing their effectiveness in classifying CT scan lung images with remarkable precision-an accuracy rate of 97.5% for the Random Forest model and an AUC score that surpasses 0.99 for the SVM. Results of the model on the same data after exclusion of the topological features and on other data with application of the same model with topological features showed the efficiency of these features in the classification task.

Keywords: COVID-19 detection; Lung images; Machine learning; Topological data analysis.

Fig. 1

The flowchart for the computation of persistent homology classes

Fig. 2

An example of a pixels’ complex composed from vertices, edges and squares

Fig. 3

Example of filtration scheme of the pixels complex in Fig. 2

Fig. 4

The flowchart for PHML modeling. It entails the selection of specific cubical complexes based on the data types in use. By tuning an appropriate filtration parameter, one can apply persistent homology (PH) analysis through custom software such as PHAT. The output generated by PH is then converted into feature vectors, which are subsequently integrated with supervised machine learning methods

Fig. 5

Images (a) and (b) illustrate chest CT scans of individuals without any abnormalities, whereas images (c) and (d) represent scans of patients diagnosed with COVID-19