Mini-course: Some Examples of Data Analysis via Topological Methods

Jose A. Perea, Duke University.

Abstract: Images and time series are data types which are ubiquitous in today's information-driven world. In this mini-course we will show how shape can be found in the set of micro-images from natural scenes, and how time series data can be transformed to study periodicity and quasi-periodicity using topology. In particular, we will see how Fourier analysis on spaces of micro-images allows one to do texture classification, and how time-delay embeddings and persistence diagrams can shed light on the periodic behavior of gene networks from biological systems.