87 citations · 163 across the 9 of their papers we have counts for
10 papers · 1 filter
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…
RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds
Thibault de Surrel, Felix Hensel, Mathieu Carrière +5
The use of topological descriptors in modern machine learning applications, such as Persistence Diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potenti…
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…
Optimizing persistent homology based functions
Mathieu Carrière, Frédéric Chazal, Marc Glisse +2
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with a…