Title: TGDA Minicourse, Lecture 3: Sliding windows and persistence
Speaker: Jose Perea (Michigan State University)
Abstract: We will present in this lecture a theoretical framework for studying the persistent homology of point-clouds from time-delay (or sliding window) embeddings. We will show that persistence yields a suitable measure of periodicity at the signal level, and present theorems which relate the resulting diagrams to the choices of window size, embedding dimension and field of coefficients. We will also demonstrate how this methodology has been successfully applied to the study of periodicity in time series from gene expression data.
Seminar URL: http://www.tgda.osu.edu/tgda-seminar.html