Sliding windows and persistence
José A. Perea, Chris Traile · The Journal of the Acoustical Society of America · 2017
The use of geometric and topological ideas as a means to tackle problems in signal analysis has seen a sharp increase in the last few years. The goal of this talk is to show how ideas from dynamical systems (e.g., time delay embeddings) with tools from topological data analysis (e.g., persistent homology) allows one to extract highly non-trivial features from vector-valued time series data. As an example, we describe a paradigm for quantifying (quasi)periodicity in video data and provide applications including the study of gene regulatory networks in biology, biphonation in mammals, and speech pathologies in humans.