gGN: learning to represent graph nodes as low-rank Gaussian distributions

Unsupervised learning of node representations from knowledge graphs is critical for numerous downstream tasks, ranging from large-scale graph analysis to measuring semantic similarity between nodes. This study presents gGN as a novel representation that defines graph nodes as Gaussian distributions. Unlike existing representations that approximate such distributions using diagonal covariance matrices, our proposal approximates them using low-rank perturbations. We demonstrate that this low-rank approximation is more expressive and better suited to represent complex asymmetric relations between nodes. In addition, we provide a computationally affordable algorithm for learning the low-rank representations in an unsupervised fashion. This learning algorithm uses a novel loss function based on the reverse Kullback-Leibler divergence and two ranking metrics whose joint minimization results in node representations that preserve not only node depths but also local and global asymmetric relationships between nodes. We assessed the representation power of the low-rank approximation with an in-depth systematic empirical study. The results show that our proposal was significantly better than the diagonal approximation for preserving graph structures. Moreover, gGN also outperformed 17 methods on the downstream task of measuring semantic similarity between graph nodes.