A0262
Title: Topological signal processing
Authors: Robin Belton - Vassar College (United States) [presenting]
Abstract: The aim is to study a popular tool in topological data analysis (TDA) called sublevel set persistent homology on discrete functions through the perspective of finite ordered sets of both linearly ordered and cyclically ordered domains. The duality of filtrations of sublevel sets is proven, which undergirds a range of duality results of sublevel set persistent homology without the need to invoke continuous functions or classical Morse theory. Furthermore, aspects of the surgery of circular and linearly ordered sets are discussed, with a focus on applications in audio signal processing. It ends by discussing ideas of future work that integrate this framework with more traditional statistical techniques for analyzing time series.
