Title: Algebraic topology and the qualitative analysis of point cloud data
Time: Canceled
Abstract: Algebraic topology allows one to make precise various kinds of qualitative information ("connectivity information") about geometric objects. This kind of information can be quite useful in attempting to understand the overall structure of the space in question. The methods have mostly been restricted to situations in which one has complete information about the spaces, and have typically only been evaluated by hand. In recent years, however, methods have been developed which allow one to infer connectivity information about a geometric object even though one may only be given a finite (but large) set of points (called a point cloud) sampled from it. We will discuss these developments, and illustrate the techniques with an example from natural image statistics.