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

2020/10/17 by Nicola Quercioli, Quercioli, Nicola
Computer Science · #47H09 #54H15 #55N31 #57S10 #68U05 #Algebraic Topology (math.AT) #FOS: Mathematics #Functional Analysis (math.FA) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2010.08823

openalex publication_date 2020/10/17 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Group equivariant operators are playing a more and more relevant role in\nmachine learning and topological data analysis. In this paper we present some\nnew results concerning the construction of G-equivariant non-expansive\noperators (GENEOs) from a space varPhi of real-valued bounded continuous\nfunctions on a topological space X to varPhi itself. The space varPhi\nrepresents our set of data, while G is a subgroup of the group of all\nself-homeomorphisms of X, representing the invariance we are interested in.\n

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