Subset Node Representation Learning over Large Dynamic Graphs

TL;DR

This paper introduces DynamicPPE, a novel method for efficiently learning node embeddings for large-scale dynamic graphs, focusing on a target subset, with applications demonstrated on Wikipedia's COVID-19 pandemic data.

Contribution

DynamicPPE leverages local node embedding and dynamic personalized PageRank to efficiently learn subset node representations with properties of locality and global consistency.

Findings

Efficient per-PPV complexity of O(m * d̄ / ε) for dynamic updates.

Embeddings capture both local and global graph structure effectively.

Successful application to Wikipedia COVID-19 data shows dynamic encoding capability.

Abstract

Dynamic graph representation learning is a task to learn node embeddings over dynamic networks, and has many important applications, including knowledge graphs, citation networks to social networks. Graphs of this type are usually large-scale but only a small subset of vertices are related in downstream tasks. Current methods are too expensive to this setting as the complexity is at best linear-dependent on both the number of nodes and edges. In this paper, we propose a new method, namely Dynamic Personalized PageRank Embedding (\textsc{DynamicPPE}) for learning a target subset of node representations over large-scale dynamic networks. Based on recent advances in local node embedding and a novel computation of dynamic personalized PageRank vector (PPV), \textsc{DynamicPPE} has two key ingredients: 1) the per-PPV complexity is $\mathcal{O}(m \bar{d} / \epsilon)$ where $m,\bar{d}$, and $\epsilon$ are the number of edges received, average degree, global precision error respectively. Thus, the per-edge event update of a single node is only dependent on $\bar{d}$ in average; and 2) by using these high quality PPVs and hash kernels, the learned embeddings have properties of both locality and global consistency. These two make it possible to capture the evolution of graph structure effectively. Experimental results demonstrate both the effectiveness and efficiency of the proposed method over large-scale dynamic networks. We apply \textsc{DynamicPPE} to capture the embedding change of Chinese cities in the Wikipedia graph during this ongoing COVID-19 pandemic (https://en.wikipedia.org/wiki/COVID-19_pandemic). Our results show that these representations successfully encode the dynamics of the Wikipedia graph.