Invariant Representations of Embedded Simplicial Complexes

2023/02/27 by Taejin Paik, Paik, Taejin
Computer Science · #55N31 #68T07 #Algebraic Topology (math.AT) #Artificial Intelligence (cs.AI) #Computational Geometry (cs.CG) #Data Management and Algorithms #Data Visualization and Analytics #FOS: Computer and information sciences #FOS: Mathematics #I.2.6 #I.5.1 #I.5.2 #Machine Learning (cs.LG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2302.13565

openalex publication_date 2023/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Analyzing embedded simplicial complexes, such as triangular meshes and graphs, is an important problem in many fields. We propose a new approach for analyzing embedded simplicial complexes in a subdivision-invariant and isometry-invariant way using only topological and geometric information. Our approach is based on creating and analyzing sufficient statistics and uses a graph neural network. We demonstrate the effectiveness of our approach using a synthetic mesh data set.

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