4 papers · 1 filter
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…
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…