Invariant Representations of Embedded Simplicial Complexes

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Publication date: 27 February 2023

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.

Has companion code repository: https://github.com/tjpaik/invariantrepresentation

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