SIGEM: A Simple yet Effective Similarity based Graph Embedding Method

In the literature, various graph embedding methods have been proposed. Although they have pioneered notable techniques in the field, we point out their four drawbacks as follows: (1) inability to consider global graph structure(2) undermining learning quality(3) impairing in/out-degree distributions in directed graphs, and (4) limited applicability. Inspired by these drawbacks, we first propose LINOW, a recursive LI nk-based similarity measure for graphs by utilizing NO des' Weights, which is applicable to both directed and undirected graphs. Then, we provide a matrix form that dramatically accelerates LINOW's computation without approximation. Furthermore, to enhance its scalability, we provide two variants, LINOW-sn and LINOW-bn, to compute similarity scores w.r.t. a single node and a batch of nodes, respectively. Finally, we propose SIGEM, a simple yet effective self-supervised and contrastive-free SI milarity based Graph EM bedding method that employs LINOW-bn to compute similarity scores of nodes in the graph, thereby ranking them. Then, it tries to preserve the original ranks of nodes in the graph within their corresponding vectors in the embedding space, by employing a single-layer neural network. The results of our extensive experiments with eight real-world datasets and thirteen state-of-the-art and conventional embedding methods demonstrate that (1) LINOW-sn and LINOW-bn successfully improve the scalability of naive LINOW(2) LINOW is beneficial to similarity based graph embedding, and (3) SIGEM consistently achieves the highest accuracy in both graph reconstruction and node classification tasks compared to other methods, while it significantly outperforms them in most cases of the link prediction task.