Studying the Effect of GNN Spatial Convolutions On The Embedding Space’s Geometry

The objective of this paper is to answer three questions: (a) how does the choice of a particular convolution operator affect the organisation of the embedding space, (b) how does it relate to the original properties (i.e. node features, graph distances or topological attributes), and (c) what is the most appropriate convolution operator for a given dataset? We will attempt and answer all three questions by studying two larger families of row-normalized and symmetrized convolution operators (parametrized by the variables $\alpha \in [0,1]$ and $\beta \in \mathbb{R}^+$), allowing us to show how the convolution operator itself is in fact tunable. In particular, we will show different values of α and βimpact the organization of the latent space and the inherent geometry of the embeddings. Finally, we will characterize regimes in which certain choices of operators might be more relevant than others.

The poster is ready to be presented at UAI 2023.