5 papers
Persistent Homology and Equivariance in Data Analysis: A Topological Introduction
Patrizio Frosini, Ulderico Fugacci, Nicola Quercioli +1
This new book is intended as a first elementary introduction to Topological Data Analysis for mathematics students seeking a rigorous account of the foundations of persistent homol…
The Convex Matching Distance in Multiparameter Persistence
Francesco Conti, Patrizio Frosini, Ulderico Fugacci +4
We introduce the convex matching distance, a novel metric for comparing functions with values in the real plane. This metric measures the maximal bottleneck distance between the pe…
An Algebraic Representation Theorem for Linear GENEOs in Geometric Machine Learning
Francesco Conti, Patrizio Frosini, Nicola Quercioli
Geometric and Topological Deep Learning are rapidly growing research areas that enhance machine learning through the use of geometric and topological structures. Within this framew…
Reconstruction of SINR Maps from Sparse Measurements using Group Equivariant Non-Expansive Operators
Lorenzo Mario Amorosa, Francesco Conti, Nicola Quercioli +4
As sixth generation (6G) wireless networks evolve, accurate signal-to-interference-noise ratio (SINR) maps are becoming increasingly critical for effective resource management and…
Matching distance via the extended Pareto grid
Patrizio Frosini, Eloy Mósig GarcÃa, Nicola Quercioli +1
One of the most animated themes of multidimensional persistence is the comparison between invariants. The matching distance between persistent Betti numbers functions (or rank inva…