87 citations · 317 across the 22 of their papers we have counts for
31 papers
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.,…
On the bottleneck stability of rank decompositions of multi-parameter persistence modules
Magnus Bakke Botnan, Steffen Oppermann, Steve Oudot +1
A significant part of modern topological data analysis is concerned with the design and study of algebraic invariants of poset representations -- often referred to as multi-paramet…
On the stability of multigraded Betti numbers and Hilbert functions
Steve Oudot, Luis Scoccola
Multigraded Betti numbers are one of the simplest invariants of multiparameter persistence modules. This invariant is useful in theory -- it completely determines the Hilbert funct…
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…
Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions
Magnus Bakke Botnan, Steffen Oppermann, Steve Oudot
In this paper, we introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally…
Local characterizations for decomposability of 2-parameter persistence modules
Magnus Bakke Botnan, Vadim Lebovici, Steve Oudot
We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the index…