Optimization of Spectral Wavelets for Persistence-Based Graph Classification

Autor: Ka Man Yim, Jacob Leygonie

Publikováno v: Frontiers in Applied Mathematics and Statistics, Vol 7 (2021)

A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimizes the choice of wavelet for a dataset of graphs, such that their associated persist

Externí odkaz: https://doaj.org/article/ca232f2d4d3b45cdb6658a249aaa5b1e

A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis

Autor: Jacob Leygonie, Mathieu Carrière, Théo Lacombe, Steve Oudot

We introduce a novel gradient descent algorithm refining the well-known Gradient Sampling algorithm on the class of stratifiably smooth objective functions, which are defined as locally Lipschitz functions that are smooth on some regular pieces—cal

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04a77b31e3c52c1408af58b93d184103
http://arxiv.org/abs/2109.00530

A Framework for Differential Calculus on Persistence Barcodes

Autor: Jacob Leygonie, Steve Oudot, Ulrike Tillmann

Publikováno v: Foundations of Computational Mathematics
Foundations of Computational Mathematics, Springer Verlag, 2021
Foundations of Computational Mathematics, 2021, ⟨10.1007/s10208-021-09522-y⟩

We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to the space of ordered barcodes, from which derivatives can be computed.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a0dfe31f7db1b43c5153ad7f527426b
http://arxiv.org/abs/1910.00960