Simplicial Complex Representation Learning

Simplicial complexes form an important class of topological spaces that are frequently used to in many applications areas such as computer-aided design, computer graphics, and simulation. The representation learning on graphs, which are just 1-d simplicial complexes, has witnessed a great attention and success in the past few years. Due to the additional complexity higher dimensional simplicial hold, there has not been enough effort to extend representation learning to these objects especially when it comes to learn entire-simplicial complex representation. 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 utilizes a simplex-level embedding induced by a pre-trained simplicial autoencoder to learn an entire simplicial complex representation. To the best of our knowledge, this work presents the first method for learning simplicial complex-level representation.