8 papers
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…
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. Despite these advantages, it has seld…
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…
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…
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…