22 citations · 55 across the 5 of their papers we have counts for
6 papers
Wasserstein convergence of Čech persistence diagrams for samplings of submanifolds
Charles Arnal, David Cohen-Steiner, Vincent Divol
Čech Persistence diagrams (PDs) are topological descriptors routinely used to capture the geometry of complex datasets. They are commonly compared using the Wasserstein distances $…
Critical points of the distance function to a generic submanifold
Charles Arnal, David Cohen-Steiner, Vincent Divol
In general, the critical points of the distance function to a compact submanifold can be poorly behaved. In this article, we show…
Estimation and Quantization of Expected Persistence Diagrams
Vincent Divol, Théo Lacombe
Persistence diagrams (PDs) are the most common descriptors used to encode the topology of structured data appearing in challenging learning tasks; think e.g. of graphs, time series…
Understanding the Topology and the Geometry of the Space of Persistence Diagrams via Optimal Partial Transport
Vincent Divol, Théo Lacombe
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence dia…
On the choice of weight functions for linear representations of persistence diagrams
Vincent Divol, Wolfgang Polonik
Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly…
The density of expected persistence diagrams and its kernel based estimation
Frédéric Chazal, Vincent Divol
Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discre…