87 citations · 322 across the 21 of their papers we have counts for
22 papers
Building confidence regions for Reeb graphs using the interleaving distance
Matteo Pegoraro, Alberto Conforti, Mathieu Carrière
We develop confidence regions for Reeb graphs from finite samples using the interleaving distance. Given a point cloud equipped with a filter function, we construct a finite proxim…
TopoFisher: Learning Topological Summary Statistics by Maximizing Fisher Information
Matteo Biagetti, Mathieu Carrière, Francesco Conti +3
Persistence diagrams provide stable, interpretable summaries of geometric and topological structure and are useful for simulation-based inference when low-order statistics miss key…
Persistence-based topological optimization: a survey
Mathieu Carriere, Yuichi Ike, Théo Lacombe +1
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can…
Differentiability and Optimization of Multiparameter Persistent Homology
Luis Scoccola, Siddharth Setlur, David Loiseaux +2
Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topol…
A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions
David Loiseaux, Mathieu Carrière, Andrew J. Blumberg
Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets…
Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures
David Loiseaux, Luis Scoccola, Mathieu Carrière +2
Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g.,…