87 citations · 317 across the 22 of their papers we have counts for
12 papers · 1 filter
A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis
Jacob Leygonie, Mathieu Carrière, Théo Lacombe +1
We introduce a novel gradient descent algorithm extending the well-known Gradient Sampling methodology to the class of stratifiably smooth objective functions, which are defined as…
Intrinsic Interleaving Distance for Merge Trees
Ellen Gasparovic, Elizabeth Munch, Steve Oudot +3
Merge trees are a type of graph-based topological summary that tracks the evolution of connected components in the sublevel sets of scalar functions. They enjoy widespread applicat…
Sliced Wasserstein Kernel for Persistence Diagrams
Mathieu Carrière, Marco Cuturi, Steve Oudot
Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy…
Statistical Analysis and Parameter Selection for Mapper
Mathieu Carrière, Bertrand Michel, Steve Oudot
In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal…
Local Equivalence and Intrinsic Metrics between Reeb Graphs
Mathieu Carrière, Steve Oudot
As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics betwe…
Computing Zigzag Persistent Cohomology
Clément Maria, Steve Oudot
Zigzag persistent homology is a powerful generalisation of persistent homology that allows one not only to compute persistence diagrams with less noise and using less memory, but a…