3 citations · 5 across the 11 of their papers we have counts for
12 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…
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…
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…
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 García, 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…
A topological model for partial equivariance in deep learning and data analysis
Lucia Ferrari, Patrizio Frosini, Nicola Quercioli +1
In this article, we propose a topological model to encode partial equivariance in neural networks. To this end, we introduce a class of operators, called P-GENEOs, that change data…
Geometry of the matching distance for 2D filtering functions
Marc Ethier, Patrizio Frosini, Nicola Quercioli +1
In this paper we exploit the concept of extended Pareto grid to study the geometric properties of the matching distance for -valued regular functions defined on a Rie…
On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operators
Pasquale Cascarano, Patrizio Frosini, Nicola Quercioli +1
Group equivariant non-expansive operators have been recently proposed as basic components in topological data analysis and deep learning. In this paper we study some geometric prop…
Some new methods to build group equivariant non-expansive operators in TDA
Nicola Quercioli
Group equivariant operators are playing a more and more relevant role in machine learning and topological data analysis. In this paper we present some new results concerning the co…
On the finite representation of group equivariant operators via permutant measures
Giovanni Bocchi, Stefano Botteghi, Martina Brasini +2
The study of -equivariant operators is of great interest to explain and understand the architecture of neural networks. In this paper we show that each linear -equivariant op…
Landscapes of data sets and functoriality of persistent homology
Wojciech Chacholski, Alessandro De Gregorio, Nicola Quercioli +1
The aim of this article is to describe a new perspective on functoriality of persistent homology and explain its intrinsic symmetry that is often overlooked. A data set for us is a…
Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning
Mattia G. Bergomi, Patrizio Frosini, Daniela Giorgi +1
The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context. The framework builds on a synergy between persistent ho…