An Introduction to Topological Data Analysis with the Topology ToolKit
Julien Tierny, Sorbonne Université
Topological Data Analysis (TDA) is a recent area of computer science that focuses on discovering intrinsic structures hidden in data. Based on solid mathematical tools such as Morse theory and Persistent Homology, TDA enables the robust extraction of the main features of a data set into stable, concise, and multi-scale descriptors that facilitate data analysis and visualization. In this talk, I will give an intuitive overview of the main tools used in TDA (persistence diagrams, Reeb graphs, Morse-Smale complexes, etc) with applications to concrete use cases in computational fluid dynamics, medical imaging, quantum chemistry, and climate modeling. This talk will be illustrated with results produced with the "Topology ToolKit" (TTK), an open-source library (BSD license) that we develop with collaborators to showcase our research. Tutorials for re-producing these experiments are available on the TTK website.
Julien Tierny received the Ph.D. degree in Computer Science from the University of Lille in 2008 and the Habilitation degree (HDR) from Sorbonne University in 2016. He is currently a CNRS permanent research scientist, affiliated with Sorbonne University (Paris, France). Prior to his CNRS tenure, he held a Fulbright fellowship (U.S. Department of State) and was a post-doctoral researcher at the Scientific Computing and Imaging Institute at the University of Utah. His research expertise lies in topological methods for data analysis and visualization. He co-authored two books on the topic and received several awards for his research, including best paper awards. He regularly serves as an international program committee member for the top venues in data visualization (IEEE VIS, EuroVis, etc.) and he is an associate editor for IEEE Transactions on Visualization and Computer Graphics. In late 2019, he was awarded a consolidator grant by the ERC. Julien Tierny is also the founder and lead developer of the Topology ToolKit (TTK), an open source library for topological data analysis.