5 citations · 6 across the 6 of their papers we have counts for
6 papers
Certifying Robustness via Topological Representations
Jens Agerberg, Andrea Guidolin, Andrea Martinelli +3
We propose a neural network architecture that can learn discriminative geometric representations of data from persistence diagrams, common descriptors of Topological Data Analysis.…
On the support of Betti tables of multiparameter persistent homology modules
Andrea Guidolin, Claudia Landi
Persistent homology encodes the evolution of homological features of a multifiltered cell complex in the form of a multigraded module over a polynomial ring, called a multiparamete…
Algebraic Wasserstein distances and stable homological invariants of data
Jens Agerberg, Andrea Guidolin, Isaac Ren +1
Distances have a ubiquitous role in persistent homology, from the direct comparison of homological representations of data to the definition and optimization of invariants. In this…
Koszul complexes and relative homological algebra of functors over posets
Wojciech Chacholski, Andrea Guidolin, Isaac Ren +2
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of…
Morse inequalities for the Koszul complex of multi-persistence
Andrea Guidolin, Claudia Landi
In this paper, we define the homological Morse numbers of a filtered cell complex in terms of relative homology of nested filtration pieces, and derive inequalities relating these…
Computing higher Leray-Serre spectral sequences of towers of fibrations
Andrea Guidolin, Ana Romero
The higher Leray-Serre spectral sequence associated with a tower of fibrations represents a generalization of the classical Leray-Serre spectral sequence of a fibration. In this wo…