3 papers
math.FA2020
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…
math.AT2020
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…
cs.LG2018
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…