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.

网络嵌入旨在将网络中所有节点的拓扑邻近性映射到低维表示空间中。先前的研究主要集中在保留网络的层内结构（例如一阶邻近度，二阶邻近度和社区结构）上。但是，许多复杂的网络通常采用层次结构社区结构的形式呈现层次结构。如何有效地保持多粒度下的内部结构和层次化社区结构是一个有意义而又艰巨的任务。受到“颗粒计算”的启发，“颗粒计算”是一个深深植根于人类在多颗粒度下感知现实世界的思维能力的解决问题的概念，我们通过在多粒度下保留网络的层内结构和分层社区结构，提出了一种统一的网络嵌入框架，称为网络嵌入的层次结构社区结构保留方法。首先，通过网络粒度构造从细到粗的不同粒度网络，揭示了原始网络的分层社区结构。其次，从细到细，精细网络继承了细粒度网络的嵌入，作为细化过程中良好的初始化嵌入，使得嵌入在多粒度下保留了网络的层内结构和分层社区结构。最后，将每个节点的学习知识嵌入到下游任务中，包括多标签分类和网络可视化。实验结果表明，HCNE明显优于其他最新技术。同时，我们直观地展示了HCNE在网络可视化方面的有效性，它可以在多粒度的情况下保留网络的层内结构和分层社区结构。