Hybrid Embedding via Cross-layer Random Walks on Multiplex Networks

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.