9 papers
Building confidence regions for Reeb graphs using the interleaving distance
Matteo Pegoraro, Alberto Conforti, Mathieu Carrière
We develop confidence regions for Reeb graphs from finite samples using the interleaving distance. Given a point cloud equipped with a filter function, we construct a finite proxim…
Circular Max-Flow for Periodic Data via Reeb Graphs
Matteo Pegoraro, Lisbeth Fajstrup
We introduce a max-flow framework for data with periodic boundary conditions, motivated by the analysis of transport in atomistic materials. Starting from a space X equipped with a…
Persistence Spheres: a Bi-continuous Linear Representation of Measures for Partial Optimal Transport
Matteo Pegoraro
We improve and extend persistence spheres, introduced in~\cite{pegoraro2025persistence}. Persistence spheres map an integrable measure on the upper half-plane, including persi…
Persistence Spheres: Bi-continuous Representations of Persistence Diagrams
Matteo Pegoraro
We introduce persistence spheres, a novel functional representation of persistence diagrams. Unlike existing embeddings (such as persistence images, landscapes, or kernel methods),…
A Persistence-Driven Edit Distance for Trees with Abstract Weights
Matteo Pegoraro
In this work we define a novel edit distance for trees considered with some abstract weights on the edges. The metric is driven by the idea of considering trees as topological summ…
A Finitely Stable Edit Distance for Functions Defined on Merge Trees
Matteo Pegoraro
In this work we define a metric structure to compare functions defined on different merge trees. The metric introduced possesses some stability properties, which we illustrate with…