no code implementations • 25 Aug 2023 • Lucia Ferrari, Patrizio Frosini, Nicola Quercioli, Francesca Tombari
In this article, we propose a topological model to encode partial equivariance in neural networks.
no code implementations • 13 Jun 2023 • Diogo Lavado, Cláudia Soares, Alessandra Micheletti, Giovanni Bocchi, Alex Coronati, Manuel Silva, Patrizio Frosini
In this paper, we propose SCENE-Net, a low-resource white-box model for 3D point cloud semantic segmentation.
no code implementations • 29 Jun 2022 • Faraz Ahmad, Massimo Ferri, Patrizio Frosini
In this paper we establish a bridge between Topological Data Analysis and Geometric Deep Learning, adapting the topological theory of group equivariant non-expansive operators (GENEOs) to act on the space of all graphs weighted on vertices or edges.
no code implementations • 31 Jan 2022 • Giovanni Bocchi, Patrizio Frosini, Alessandra Micheletti, Alessandro Pedretti, Carmen Gratteri, Filippo Lunghini, Andrea Rosario Beccari, Carmine Talarico
Nowadays there is a big spotlight cast on the development of techniques of explainable machine learning.
no code implementations • 3 Mar 2021 • Pasquale Cascarano, Patrizio Frosini, Nicola Quercioli, Amir Saki
Group equivariant non-expansive operators have been recently proposed as basic components in topological data analysis and deep learning.
no code implementations • 7 Aug 2020 • Giovanni Bocchi, Stefano Botteghi, Martina Brasini, Patrizio Frosini, Nicola Quercioli
This result makes available a new method to build linear $G$-equivariant operators in the finite setting.
1 code implementation • 31 Dec 2018 • Mattia G. Bergomi, Patrizio Frosini, Daniela Giorgi, Nicola Quercioli
The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context.
no code implementations • 7 Mar 2016 • Patrizio Frosini
In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions.
no code implementations • 27 Dec 2013 • Patrizio Frosini, Grzegorz Jablonski
In many applications concerning the comparison of data expressed by $\mathbb{R}^m$-valued functions defined on a topological space $X$, the invariance with respect to a given group $G$ of self-homeomorphisms of $X$ is required.
no code implementations • 4 Dec 2012 • Patrizio Frosini
Roughly speaking, the main idea consists in defining persistent homology by means of a set of chains that is invariant under the action of G. In this paper we formalize this idea, and prove the stability of the persistent Betti number functions in G-invariant persistent homology with respect to the natural pseudo-distance d_G.