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

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 a-random walk model with two main contributions. Firstly, the traditional random walk sampling reveals instability. Thus, we associate a parameter a 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 mech-anism 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 a 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 a-random walk outperforms the state-of-the-art baselines in handling small and large graphs.& COPY; 2023 Elsevier Ltd. All rights reserved.