Graph embedding via multi-scale graph representations

Graph embedding provides an effective way to encode graph nodes as continuous vector representations in a low-dimensional space. The high-order proximities based graph embedding methods can preserve global structures, but the high-order proximities based objectives typically imply non-convex optimization and high computational complexity. In contrast, the low-order proximities based graph embedding methods evade the definition and optimization of complex high-order proximities based objectives, but cannot capture global structures. Furthermore, numerous graph embedding methods that only consider the proximity relationships among nodes ignore to capture global structure from the perspective of subgraphs. Motivated by this, we propose a novel graph embedding framework via multi-scale graph representations, named MSGE. MSGE first determines multiple subgraphs of different scales based on random walk. At each scale, MSGE generates a new graph by creating edges among the subgraphs which are treated as supernodes. Thus, the generated multi-scale graphs can approximate rich global structure of the original graph. MSGE then employs any existing graph embedding method as a black box to learn subgraph (i.e., supernode) embeddings on each generated graph. Subsequently, a first-order proximity based embedding fusion method is devised to yield node embeddings of the original graph via the learned multi-scale subgraph embeddings. Finally, we apply MSGE on four classical graph embedding methods and extensive experimental results demonstrate that our framework can generate embeddings of better quality and significantly outperform the original graph embedding methods on visualization, node classification and community detection tasks. (c) 2021 Elsevier Inc. All rights reserved.