10 papers
The sublevel Flood bifiltration: towards scalable 2-parameter persistent homology
Mattéo Clémot, Julie Digne, Julien Tierny
Multiparameter persistent homology is a rapidly developing branch of topological data analysis that improves the robustness of single-parameter persistent homology to outliers, whi…
Sierpiński--Knopp Wasserstein Distance for Persistence Diagrams and Applications to 2-Wasserstein Approximation
Sebastien Tchitchek, Julien Tierny
This paper introduces the Sierpiński-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams. The SK-Wasserstein distance, denoted , maps diagr…
Delaunay-Rips filtration: a study and an algorithm
Mattéo Clémot, Julie Digne, Julien Tierny
The Delaunay-Rips filtration is a lighter and faster alternative to the well-known Rips filtration for low-dimensional Euclidean point clouds, making it a promising tool for topolo…
Continuous Edit Distance, Geodesics and Barycenters of Time-varying Persistence Diagrams
Sebastien Tchitchek, Mohamed Kissi, Julien Tierny
We introduce the Continuous Edit Distance (CED), a geodesic and elastic distance for time-varying persistence diagrams (TVPDs). The CED extends edit-distance ideas to TVPDs by comb…
Robust Barycenters of Persistence Diagrams
Keanu Sisouk, Eloi Tanguy, Julie Delon +1
This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic…
Topology Aware Neural Interpolation of Scalar Fields
Mohamed Kissi, Keanu Sisouk, Joshua A. Levine +1
This paper presents a neural scheme for the topology-aware interpolation of time-varying scalar fields. Given a time-varying sequence of persistence diagrams, along with a sparse t…
Distributed Discrete Morse Sandwich: Efficient Computation of Persistence Diagrams for Massive Scalar Data
Eve Le Guillou, Pierre Fortin, Julien Tierny
The persistence diagram, which describes the topological features of a dataset, is a key descriptor in Topological Data Analysis. The "Discrete Morse Sandwich" (DMS) method has bee…
BondMatcher: H-Bond Stability Analysis in Molecular Systems
Thomas Daniel, Malgorzata Olejniczak, Julien Tierny
This application paper investigates the stability of hydrogen bonds (H-bonds), as characterized by the Quantum Theory of Atoms in Molecules (QTAIM). First, we contribute a database…
Topological Autoencoders++: Fast and Accurate Cycle-Aware Dimensionality Reduction
Mattéo Clémot, Julie Digne, Julien Tierny
This paper presents a novel topology-aware dimensionality reduction approach aiming at accurately visualizing the cyclic patterns present in high dimensional data. To that end, we…
A User's Guide to Sampling Strategies for Sliced Optimal Transport
Keanu Sisouk, Julie Delon, Julien Tierny
This paper serves as a user's guide to sampling strategies for sliced optimal transport. We provide reminders and additional regularity results on the Sliced Wasserstein distance.…