Maximal Coding Rate Reduction for Graph Embeddings

Abstract

Despite the recent prosperity in the graph representation learning Graph Neural Network (GNN) community, most research fails to extend their analysis to the learned representations for the graph data. They overlook the structural composition of the graph data in high-dimensional manifolds, which reduces the discriminative power and interpretability of the learned representations.

The idea to capture the semantics in the complex graph data does not receive sufficient attention. Due to the lack of a theoretical framework to efficiently and effectively learn from the graph data and produce physically meaningful and discriminative graph embeddings, this Honours thesis explores the application of the principle of Maximal Coding Rate Reduction (MCR2) to graph representation learning through designing a novel GNN model. The proposed model focuses on the structures of graphs, identifying different subspaces underlying the graphical data. Based on the structures, the subspace representations will be optimised by the principle of MCR2 to become the optimal graph representations. The effectiveness and properties of the proposed model are validated through experiments. This work opens avenues for further research in graph representation learning under the principle of MCR2.