Hierarchical community structure preserving approach for network embedding

Network embedding aims to map the topological proximities of all nodes in a network into a low-dimensional representation space. Previous studies mainly focus on preserving the within-layer structure of the network (such as first-order proximities, second-order proximities, and community structure). However, many complex networks present a hierarchical organization, often in the form of a hierarchy community structure. How to effectively preserve the within-layer structure and the hierarchical community structure under multi granularity is a meaningful and still tough task. Inspired by Granular Computing, which is a problem-solving concept deeply rooted in human thinking ability to perceive the real world under multi-granularity, we propose a unified network embedding framework by preserving both the within-layer structure and the hierarchical community structure of the network under multi-granularity, named as Hierarchical Community structure preserving approach for Network Embedding (HCNE). Firstly, different granular networks from fine to coarse are constructed by network granulation which reveals the hierarchical community structure of the original network. Secondly, from coarse to fine, finer networks inherit the embedding of coarse-grained networks as good initialization embedding in the refinement process so that the embedding preserved both the within-layer structure and the hierarchical community structure of the network under multi-granularity. Finally, the learned embedding of each node fed into downstream tasks, including multi label classification and network visualization. Experimental results demonstrate that HCNE significantly outperforms other state-of-the-art methods. Meanwhile, we intuitively show the effectiveness of HCNE on network visualization which can preserve both the within-layer structure and the hierarchical community structure of the network under multi-granularity. (c) 2020 Elsevier Inc. All rights reserved.