Invariant Representations of Embedded Simplicial Complexes

TL;DR

This paper introduces a novel method for analyzing embedded simplicial complexes that is invariant to subdivisions and isometries, leveraging topological and geometric features with graph neural networks.

Contribution

It presents a new approach that combines topological invariants and graph neural networks for analyzing embedded simplicial complexes.

Findings

Effective on synthetic mesh data

Invariant to subdivision and isometry

Utilizes topological and geometric information

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.