Recently, network embedding has received a large amount of attention in network analysis. Although some network embedding methods have been developed from different perspectives, on one hand, most of the existing methods only focus on leveraging the plain network structure, ignoring the abundant attribute information of nodes. On the other hand, for some methods integrating the attribute information, only the lower-order proximities (e.g., microscopic proximity structure) are taken into account, which may suffer if there exists the sparsity issue and the attribute information is noisy. To overcome this problem, the attribute information and mesoscopic community structure are utilized. In this article, we propose a novel network embedding method termed Attributed Network Embedding with Micro-Meso structure, which is capable of preserving both the attribute information and the structural information including the microscopic proximity structure and mesoscopic community structure. In particular, both the microscopic proximity structure and node attributes are factorized by Nonnegative Matrix Factorization (NMF), from which the low-dimensional node representations can be obtained. For the mesoscopic community structure, a community membership strength matrix is inferred by a generative model (i.e., BigCLAM) or modularity from the linkage structure, which is then factorized by NMF to obtain the low-dimensional node representations. The three components are jointly correlated by the low-dimensional node representations, from which two objective functions (i.e., ANEM_B and ANEM_M) can be defined. Two efficient alternating optimization schemes are proposed to solve the optimization problems. Extensive experiments have been conducted to confirm the superior performance of the proposed models over the state-of-the-art network embedding methods.

中文翻译：

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具有微细观结构的归因网络嵌入

最近，网络嵌入在网络分析中受到了大量关注。尽管已经从不同的角度发展了一些网络嵌入方法，但一方面，现有的方法大多只关注于利用简单的网络结构，而忽略了节点丰富的属性信息。另一方面，对于一些集成属性信息的方法，只考虑低阶邻近性（例如，微观邻近结构），如果存在稀疏性问题并且属性信息有噪声，则可能会受到影响。为了克服这个问题，利用了属性信息和介观社区结构。在本文中，我们提出了一种新的网络嵌入方法，称为具有微细观结构的属性网络嵌入，它既能保存属性信息，也能保存微观邻近结构和介观群落结构等结构信息。特别是，微观邻近结构和节点属性都通过非负矩阵分解（NMF）分解，从中可以获得低维节点表示。对于细观社区结构，社区成员强度矩阵由生成模型（即BigCLAM）或链接结构的模块性推断，然后通过NMF分解以获得低维节点表示。这三个分量通过低维节点表示联合相关，从中可以定义两个目标函数（即ANEM_B 和ANEM_M）。提出了两种有效的交替优化方案来解决优化问题。已经进行了广泛的实验，以确认所提出的模型在最先进的网络嵌入方法上的优越性能。