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