Unifying Structural Proximity and Equivalence for Network Embedding

Benyun Shi,Chunpeng Zhou,Jiming Liu,Xiaobin Xu,Hongjun Qiu

doi:10.1109/access.2019.2932396

Abstract

The fundamental purpose of network embedding is to automatically encode each node in a network as a low-dimensional vector, while at the same time preserving certain characteristics of the network. Based on the nodes' embeddings, downstream network analytic tasks such as community mining, node classification, and link prediction, can then be easily implemented using traditional machine learning methods. In recent years, extensive network embedding methods have been proposed based on factorization, random walks, deep learning, and so on. However, most of them focus mainly on preserving the structural proximity of network nodes, where highly interconnected nodes in a network will be represented closely together in the embedded vector space. While in many real-world networks, existing studies have revealed that high-order organizations (e.g., network motifs and graphlets) may be related to specific network functions. In this case, nodes far apart but with a similar organization in a network (i.e., structural equivalence) may have similar network functions. Accordingly, in this paper, we present a hybrid embedding method that unifies both structural proximity and equivalence (SPaE) of a network. Specifically, we adopt the concept of graphlet degree vector (GDV) to measure structural equivalence between network nodes. Through carrying out experiments on both synthetic and real-world datasets, we evaluate the performance of the hybrid embedding method in tasks of node clustering, node classification, and visualization. The results demonstrate that the proposed SPaE method outperforms several state-of-the-art methods when the network analytic tasks are not merely related to structural proximity. Finally, we also conduct experiments to evaluate the flexibility, robustness, and parameter sensitivity of the hybrid embedding method.

Highlights

Networks have been widely used to describe a group of interconnected objects in many fields, such as social networks [1], food webs [2], neuronal networks [3], power grids [4], protein-protein interaction networks [5], and the World Wide Web [6]
To preserve the structural equivalence between network nodes, the objective is to learn a mapping function f2 : i → vi ∈ Rd (d n) such that vi and vj in the embedded space V preserve the cosine similarity sij between nodes i and j. Taking into consideration both structural proximity and functional roles of network nodes, in this paper, we focus on the problem of how to unify them simultaneously to preserve both structural proximity and equivalence for network embedding
2) RESULTS ON THE (MIRRORED) KARATE NETWORK we evaluate the capability of the SPaE method with respect to preserving structural proximity and equivalence, on the karate network and mirrored karate network, respectively

Summary

Introduction

Networks have been widely used to describe a group of interconnected objects in many fields, such as social networks [1], food webs [2], neuronal networks [3], power grids [4], protein-protein interaction networks [5], and the World Wide Web [6]. Due to the ubiquity of networks in countless real-world systems, many network analytic tasks have been proposed to help understand the underlying characteristics of complex systems. In the past few decades, a great number of approaches have been proposed to tackle the above-mentioned network analytic tasks by operating directly on the original network adjacency matrix. The network embedding approach has attracted lots of attention, the purpose of which is to automatically represent network components into a low-dimensional vector space, while at the same time preserving certain characteristics of the network [16]–[19]

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Results

Conclusion