Topological Data Analysis and Persistence Theory Applications to Heart Arrhythmia

There are over 550 million people worldwide who suffer from heart disease and related conditions. Thus, effective heart disease detection is a central discovery-driven medical problem that will help doctors make more informed decisions. Although machine learning, and specifically deep learning, has made substantial progress on developing detection algorithms, these models often become unreliable when data is excessively noisy or has minor perturbations. In recent years, a statistical analysis technique that has gradually gained popularity is that of topological data analysis, where tools from algebraic topology are applied in a statistical setting. This technique is less sensitive to noise than standard machine learning. We study uses of topological data analysis and a sub-topic known as persistence theory to analyze ECG data of patients suffering from a heart condition known as arrhythmia, a form of abnormal cardiac beating. We use topological properties obtained from our analysis to differentiate between arrhythmia patients and healthy controls and use these properties to provide an alternative arrhythmia detection algorithm from the existing literature.