Persistence Landscape of Functional Signal and Its Application to Epileptic Electroencaphalogram Data

Abstract Persistent homology is a recently popular multi-scale topological data analysis framework that has many potential scientific applications, particularly in neuroscience. The method can be effectively applied to yield patterns in nonlinear imaging data that are otherwise undetected by existing mono-scale techniques. Among several persistent homological features, recently proposed persistence landscape is used as a new signal detection method in one-dimensional functional data. For this purpose, weighted Fourier series expansion is used for estimating the functional shape of the data before the persistent landscape is obtained. We utilize the proposed method to study topological differences between electroencaphalogram (EEG) data during pre-seizure and seizure periods in a patient diagnosed with left temporal epilepsy.