Some new methods to build group equivariant non-expansive operators in TDA

Abstract: 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 construction of $G$-equivariant non-expansive operators (GENEOs) from a space $\varPhi$ of real-valued bounded continuous functions on a topological space $X$ to $\varPhi$ itself. The space $\varPhi$ represents our set of data, while $G$ is a subgroup of the group of all self-homeomorphisms of $X$, representing the invariance we are interested in.