Invariant Representations of Embedded Simplicial Complexes
This work addresses the analysis of embedded simplicial complexes for fields such as computational geometry and machine learning, but it appears incremental as it builds on existing methods like graph neural networks.
The paper tackles the problem of analyzing embedded simplicial complexes like triangular meshes and graphs by proposing a new approach that is subdivision-invariant and isometry-invariant, using topological and geometric information with a graph neural network, and demonstrates its effectiveness on a synthetic mesh dataset.
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.