Formula omitted]-Random Walk: Collaborative sampling and weighting mechanisms based on a single parameter for node embeddings

Abstract

Graph embedding transforms a graph into vector representations to facilitate subsequent graph-analytic tasks. Existing graph embedding methods ignore efficient node sampling and intelligent node weighting, leading to a weak node representation.This paper introduces the β-random walk model with two main contributions. Firstly, the traditional random walk sampling reveals instability. Thus, we associate a parameter β with each node to balance and stabilize the sampling process, producing high-efficient trajectories. Secondly, we design a weighting mechanism that incorporates these trajectories to generate accurate representations. The designed mechanism models the behavior of each node contextually at each episode, considering the current state and the previous weights to produce the next episode’s weights. The parameter β optimizes the node weights by simulating multiple high-order proximity walks from each node. This approach provides summarized insights about each node’s behavior and its neighbors’ context, which enables a consistent discovery of prominent paths variation in the graph.Experimental results demonstrate that the β-random walk outperforms the state-of-the-art baselines in handling small and large graphs.