GraRep++: Flexible Learning Graph Representations With Weighted Global Structural Information

Abstract

The key to vertex embedding is to learn low-dimensional representations of global graph information, and integrating information from multiple steps is an effective strategy. Existing research shows that the transition probability of each step can capture the relationship between different hops, and the graph’s global information can be obtained simultaneously. However, much of the current work simply concatenates representations of different hops into a global representation. In other words, they are unclear about the contribution of each $k$ -step ( $k\geq {1}$ ) structural information in the embedding. With this motivation, we propose a unified framework that focuses on considering the contributions of different steps in global graph representation. It reconsiders the contribution of different steps in the global representation from two perspectives: (i)We flexibly assign different weights to the different steps loss function, (ii) According to different $k$ , we design strategies that all $k$ -step representations are concatenated with different proportions to form a global representation. Based on this, we more effectively integrate global structural information into the learning process. In this paper, our proposed framework achieves competitive performance on vertex classification, link prediction, and visualization tasks on multiple datasets.

Keywords

• Graph representation
• matrix factorization
• feature learning
• dimension reduction