Introduction to Topological Data Analysis and Applications
Ivan Dungan, USMA
Monday, November 13, starting at 4:00 pm, Davis 301
Refreshments at 3:30 pm, outside of Davis 216
Geometry and Topology are similar areas of math in that they both rely on a notion of "closeness", but geometry is much more rigid while topology is more relaxed. In data analysis where there is a lot of noise, geometrical spaces are much too rigid to use as models; however, topology is conducive to such conditions. We will introduce a fairly recent area of data analysis that models point-clouds with spaces in topology. The topological features (or “shape”) of a point-cloud can be qualitatively and quantitatively analyzed via topological techniques even when the data is high-dimensional or noisy. By characterizing the shape of point-clouds, we may be able to distinguish them. For example, if we have point-clouds representing biological information of cancerous tumors, we may be able to identify different subtypes.