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 $\Phi$ of real-valued bounded continuous functions on a topological space $X$ to $\Phi$ itself. The space $\Phi$ 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.