# On a New Method to Build Group Equivariant Operators by Means of Permutants

Abstract : The use of group equivariant operators is becoming more and more important in machine learning and topological data analysis. In this paper we introduce a new method to build G-equivariant non-expansive operators from a set $\varPhi$ of bounded and continuous functions $\varphi :X\rightarrow \mathbb {R}$ to $\varPhi$ itself, where X is a topological space and G is a subgroup of the group of all self-homeomorphisms of X.
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https://hal.inria.fr/hal-02060057
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Francesco Camporesi, Patrizio Frosini, Nicola Quercioli. On a New Method to Build Group Equivariant Operators by Means of Permutants. 2nd International Cross-Domain Conference for Machine Learning and Knowledge Extraction (CD-MAKE), Aug 2018, Hamburg, Germany. pp.265-272, ⟨10.1007/978-3-319-99740-7_18⟩. ⟨hal-02060057⟩

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