Node embedding aims to encode network nodes as a set of low-dimensional vectors while preserving certain structural properties of the network. In recent years, extensive studies have been conducted to preserve network communities, i.e., structural proximity of network nodes. However, few of them have focused on preserving the structural equivalence of network nodes, which describes the similarity of structural roles between network nodes. In this paper, we focus on a hybrid network embedding problem of how to flexibly and simultaneously preserve both structural proximity and equivalence. Here, we introduce the concept of graphlet degree vector (GDV) to describe structure roles of network nodes, and further measure structural equivalence based on their similarity. Specifically, we capture both structural proximity and equivalence by building a multiplex network, where both unsupervised and semi-supervised cross-layer random walk (CL-Walk) methods are implemented. By carrying out experiments on both synthetic and real-world datasets, we evaluate the performance of the proposed CL-Walk methods for the tasks of node clustering, node classification, and label prediction. The experimental results indicate that the CL-Walk method outperforms several state-of-the-art methods when both structural proximity and structural equivalence are relevant to specific network analytic task.

中文翻译：

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通过多路网络上的跨层随机游走进行混合嵌入


节点嵌入旨在将网络节点编码为一组低维向量，同时保留网络的某些结构属性。近年来，人们进行了广泛的研究来保护网络社区，即网络节点的结构邻近性。然而，很少有人关注网络节点的结构等价性，它描述了网络节点之间结构角色的相似性。在本文中，我们关注如何灵活地同时保持结构邻近性和等效性的混合网络嵌入问题。在这里，我们引入图基度向量（GDV）的概念来描述网络节点的结构角色，并根据它们的相似性进一步衡量结构等价性。具体来说，我们通过构建一个多重网络来捕获结构邻近性和等效性，其中实现了无监督和半监督跨层随机游走（CL-Walk）方法。通过在合成数据集和真实数据集上进行实验，我们评估了所提出的 CL-Walk 方法在节点聚类、节点分类和标签预测任务中的性能。实验结果表明，当结构邻近性和结构等效性都与特定网络分析任务相关时，CL-Walk 方法优于几种最先进的方法。