Different approaches to the data skeletonization problem

Given a point cloud in a Euclidean space we consider the problem of approximating the cloud by an embedded graph in the same space. We will review past approaches to related data skeletonization problems via Reeb graphs, Mapper algorithm and a 1-dimensional Homologically Persistent Skeleton. Then we will introduce a new approximate skeleton for detecting topological shapes of micelles in 3 dimensions. The talk is based on joint work with Vitaliy Kurlin at the University of Liverpool.