PhD graduated
Team : APR
Departure date : 08/31/2022

Supervision : Julien TIERNY

Progressivity in Topological Data Analysis

Topological Data Analysis (TDA) forms a collection of tools that enable the generic and efficient extraction of features in data. However, although most TDA algorithms have practicable asymptotic complexities, these methods are rarely interactive on real-life datasets, which limits their usability for interactive data analysis and visualization. In this thesis, we aimed at developing progressive methods for the TDA of scientific scalar data, that can be interrupted to swiftly provide a meaningful approximate output and that are able to refine it otherwise. First, we present a hierarchical representation of the data that enables the definition of efficient coarse-to-fine topological algorithms. As a result we introduce two progressive algorithms for the computation of the critical points and the extremum-saddle persistence diagram of a scalar field. These methods provide interpretable outputs upon interruption, offer a continuous visual feedback along the computation, and are faster in practice than their non-progressive counterpart. Next, we revisit this progressive framework to introduce an approximation algorithm for the persistence diagram of a scalar field, with strong guarantees on the related approximation error. Finally, in a effort to perform visual analysis of ensemble data, we present a novel progressive algorithm for the computation of the discrete Wasserstein barycenter of a set of persistence diagrams, a notoriously computationally intensive task. Our progressive approach enables the approximation of the barycenter within interactive times. We extend this method to a progressive, time-constraint, topological ensemble clustering algorithm. We present an application use-case of all this work in the context of supercomputing and interactive data analysis and visualization to help the urgent decision-making process during crisis events, in the scope of the European project VESTEC.

Defence : 12/08/2021

Jury members :

Michaël Aupetit, Qatar Computing Research Institute [Rapporteur]
Frédéric Chazal, INRIA [Rapporteur]
Isabelle Bloch, Sorbonne Université
David Coeurjolly, CNRS
Jean-Daniel Fekete, INRIA
Gabriel Peyré, CNRS
Vanessa Robins, Australian National University
Julien Tierny, CNRS

Departure date : 08/31/2022

2019-2023 Publications