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.

2019-2023 Publications

• 2023
  • P. Guillou, J. Vidal, J. Tierny : “Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmark”, IEEE Transactions on Visualization and Computer Graphics, pp. 1-18, (Institute of Electrical and Electronics Engineers) (2023)
  • M. Flatken, A. Podobas, R. Fellegara, A. Basermann, J. Holke, D. Knapp, M. Kontak, Ch. Krullikowski, M. Nolde, N. Brown, R. Nash, G. Gibb, E. Belikov, S. Chien, S. Markidis, P. Guillou, J. Tierny, J. Vidal, Ch. Gueunet, J. Günther, M. Pawlowski, P. Poletti, G. Guzzetta, M. Manica, A. Zardini, J.‑P. Chaboureau, M. Mendes, A. Cardil, S. Monedero, J. Ramirez, A. Gerndt : “VESTEC: Visual Exploration and Sampling Toolkit for Extreme Computing: Urgent Decision Making Meets HPC: Experiences and Future Challenges”, IEEE Access, vol. 11, pp. 87805-87834, (IEEE) (2023)
• 2022
  • Ch. Garth, Ch. Gueunet, P. Guillou, F. Iuricich, J. Levine, J. Lukasczyk, M. Pont, J. Tierny, J. Vidal, B. Wang, F. Wetzels : “Topological Analysis of Ensemble Scalar Data with TTK, A Sequel”, IEEE VIS Tutorials, Oklahoma City, United States (2022)
  • M. Pont, J. Vidal, J. Tierny : “Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)”, IEEE Transactions on Visualization and Computer Graphics, (Institute of Electrical and Electronics Engineers) (2022)
• 2021
  • J. Vidal : “Progressivité en Analyse Topologique de Données”, thesis, phd defence 12/08/2021, supervision Tierny, Julien (2021)
  • N. Brown, R. Nash, P. Poletti, G. Guzzetta, M. Manica, A. Zardini, M. Flatken, J. Vidal, Ch. Gueunet, E. Belikov, J. Tierny, A. Podobas, W. Der Chien, S. Markidis, A. Gerndt : “Utilising urgent computing to tackle the spread of mosquito-borne diseases”, IEEE/ACM HPC for Urgent Decision Making (UrgentHPC) 2021, St. Louis, United States, pp. 36-44, (IEEE) (2021)
  • M. Pont, J. Vidal, J. Delon, J. Tierny : “Wasserstein Distances, Geodesics and Barycenters of Merge Trees”, IEEE Transactions on Visualization and Computer Graphics, vol. 28 (1), pp. 291-301, (Institute of Electrical and Electronics Engineers) (2021)
  • Ch. Garth, Ch. Gueunet, P. Guillou, L. Hofmann, J. Levine, J. Lukasczyk, J. Tierny, J. Vidal, B. Wang, F. Wetzels : “Topological Analysis of Ensemble Scalar Data with TTK”, IEEE VIS Tutorials, IEEE VIS Tutorials, New Orleans, United States (2021)
  • J. Vidal, J. Tierny : “Fast Approximation of Persistence Diagrams with Guarantees”, IEEE Symposium on Large Data Analysis and Visualization, New Orleans, United States (2021)
  • J. Vidal, P. Guillou, J. Tierny : “A Progressive Approach to Scalar Field Topology”, IEEE Transactions on Visualization and Computer Graphics, vol. 27, pp. 2833-2850, (Institute of Electrical and Electronics Engineers) (2021)
• 2020
  • M. Falk, Ch. Garth, Ch. Gueunet, P. Guillou, A. Gyulassy, L. Hofmann, Ch. Kappe, J. Levine, J. Lukasczyk, J. Tierny, J. Vidal : “Topological Data Analysis Made Easy with the Topology ToolKit, What is New?”, IEEE VIS Tutorials, Salt Lake City, United States (2020)
• 2019
  • M. Kontak, J. Vidal, J. Tierny : “Statistical Parameter Selection for Clustering Persistence Diagrams”, SuperComputing Workshop on UrgentHPC, Denver, United States (2019)
  • J. Vidal, J. Budin, J. Tierny : “Progressive Wasserstein Barycenters of Persistence Diagrams”, IEEE Transactions on Visualization and Computer Graphics, (Institute of Electrical and Electronics Engineers) (2019)
  • M. Falk, Ch. Garth, Ch. Gueunet, J. Levine, J. Lukasczyk, J. Tierny, J. Vidal : “Topological Data Analysis Made Easy with the Topology ToolKit, A Sequel”, IEEE VIS Tutorials, Vancouver, Canada (2019)
  • T. Bin Masood, J. Budin, M. Falk, G. Favelier, Ch. Garth, Ch. Gueunet, P. Guillou, L. Hofmann, P. Hristov, A. Kamakshidasan, Ch. Kappe, P. Klacansky, P. Laurin, J. Levine, J. Lukasczyk, D. Sakurai, M. Soler, P. Steneteg, J. Tierny, W. Usher, J. Vidal, M. Wozniak : “An Overview of the Topology ToolKit”, TopoInVis 2019 - Topological Methods in Data Analysis and Visualization, Nykoping, Sweden (2019)