15 citations · 24 across the 9 of their papers we have counts for
5 papers · 1 filter
Algorithmic Reconstruction of the Fiber of Persistent Homology on Cell Complexes
Jacob Leygonie, Gregory Henselman-Petrusek
Let be a finite simplicial, cubical, delta or CW complex. The persistence map takes a filter as input and returns the barcodes $\math…
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…
Fiber of Persistent Homology on Morse functions
Jacob Leygonie, David Beers
Let be a Morse function on a smooth compact manifold with boundary. The path component containing of the space of Morse functions giving rise to…
The Fiber of Persistent Homology for simplicial complexes
Jacob Leygonie, Ulrike Tillmann
We study the inverse problem for persistent homology: For a fixed simplicial complex , we analyse the fiber of the continuous map on the space of filters that assi…
Optimisation of Spectral Wavelets for Persistence-based Graph Classification
Ka Man Yim, Jacob Leygonie
A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice…