Simplicial Complex Representation Learning
This addresses a gap in extending graph representation learning to more complex topological structures, which could benefit applications in computer-aided design and simulation, though it appears incremental as it builds on existing graph methods.
The paper tackles the problem of representation learning for higher-dimensional simplicial complexes, which are important in areas like computer graphics, by proposing a method that embeds entire simplicial complexes into a universal space while preserving complex-to-complex proximity, and demonstrates it on a publicly available mesh dataset.
Simplicial complexes form an important class of topological spaces that are frequently used in many application areas such as computer-aided design, computer graphics, and simulation. Representation learning on graphs, which are just 1-d simplicial complexes, has witnessed a great attention in recent years. However, there has not been enough effort to extend representation learning to higher dimensional simplicial objects due to the additional complexity these objects hold, especially when it comes to entire-simplicial complex representation learning. In this work, we propose a method for simplicial complex-level representation learning that embeds a simplicial complex to a universal embedding space in a way that complex-to-complex proximity is preserved. Our method uses our novel geometric message passing schemes to learn an entire simplicial complex representation in an end-to-end fashion. We demonstrate the proposed model on publicly available mesh dataset. To the best of our knowledge, this work presents the first method for learning simplicial complex-level representation.