Pattern Recognition and
Image Processing Group
Institute of Visual Computing and Human-Centered Technology
Title: Applied and computational topology. From applications to software and back (continuously).
In this talk I will present my recent work in applied and computational topology. Working with real data triggers out a feedback loop between problems that are interested and the software that is available/to be developed in order to solve them. I will start by presenting persistent homology as a dimension reduction technique. I will consider various patterns obtained from partial differential equations, and compute their persistence-based descriptors. I will show that the persistence descriptor carry over a lot of information about the particular partial differential equation we have analyzed. To use persistence as descriptor, we need a way to perform statistics on persistence diagrams. I will present various theoretical and software options to do that. Later, given our ability to perform statistics on persistence diagrams, I will see how to use it to scan databases of hypothetical materials that can be used for Carbon Dioxide capture and to find the best material. At the end, if time permits, I will discuss the problem of classifying different neuron trees using their persistence-based signatures. I will conclude the talk by present a Gudhi library, a new library in computational topology which aims to became the state of the art library in the community.