2021/03/03 by Pasquale Cascarano, Patrizio Frosini, Cascarano, Pasquale +5
Computer Science · Mathematics · #58D30 #62R40 #65D18 #68T09 #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Medical Image Segmentation Techniques #Morphological variations and asymmetry #Primary: 55N31 #Secondary: 58D20 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2103.02543
openalex publication_date 2021/03/03 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Group equivariant non-expansive operators have been recently proposed as basic components in topological data analysis and deep learning. In this paper we study some geometric properties of the spaces of group equivariant operators and show how a space F of group equivariant non-expansive operators can be endowed with the structure of a Riemannian manifold, so making available the use of gradient descent methods for the minimization of cost functions on F. As an application of this approach, we also describe a procedure to select a finite set of representative group equivariant non-expansive operators in the considered manifold.