107 citations · 416 across the 27 of their papers we have counts for
5 papers · 1 filter
Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space
Quentin Mérigot, Alex Delalande, Frédéric Chazal
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This emb…
ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning
Martin Royer, Frédéric Chazal, Clément Levrard +2
Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning framework…
Topological Data Analysis for Arrhythmia Detection through Modular Neural Networks
Meryll Dindin, Yuhei Umeda, Frederic Chazal
This paper presents an innovative and generic deep learning approach to monitor heart conditions from ECG signals.We focus our attention on both the detection and classification of…
PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
Mathieu Carrière, Frédéric Chazal, Yuichi Ike +3
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications…
Homotopy Reconstruction via the Cech Complex and the Vietoris-Rips Complex
Jisu Kim, Jaehyeok Shin, Frédéric Chazal +2
We derive conditions under which the reconstruction of a target space is topologically correct via the Čech complex or the Vietoris-Rips complex obtained from possibly noisy point…