SIMPLICIAL CONVOLUTIONAL NEURAL NETWORKS

Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks like graph signal reconstruction, graph or node classifications, and link prediction. However, these methods are only suitable for data defined on the nodes of a graph. In this paper, we propose a simplicial convolutional neural network (SCNN) architecture to learn from data defined on simplices, e.g., nodes, edges, triangles, etc. We study the SCNN permutation and orientation equivariance, complexity, and spectral analysis. Finally, we test the SCNN performance for imputing citations on a coauthorship complex.

Automated summary

Graphs can represent networked data using nodes and edges, and methods in signal processing and neural networks have been developed to process and learn from graph data. However, these methods are limited to data defined on nodes. This paper proposes a simplicial convolutional neural network (SCNN) architecture for learning from data defined on simplices, and studies its properties and performance on a coauthorship complex.