Topological Methods for Reasoning about Data

One of the goals of Machine Learning is to algorithmically extract non-trivial insights about data. In this lecture, I will focus on a sub-branch of Machine Learning called Topological Data Analysis (TDA) that has emerged out of the pure mathematics sub-field of Algebraic Topology. TDA methods attempt to extract such insights by considering global topological features of datasets by studying connectivity patterns between data points. I will provide a short overview of the basics of Topological Data Analysis and
will discuss current opportunities as well as challenges in applying these techniques.
I will then discuss some of our recent work in developing topologically inspired techniques with applications to motion clustering and robotic manipulation.