Graph embedding is gaining its popularity for link prediction in complex networks and achieving excellent performance. However, limited work has been done in sparse networks that represent most of real networks. In this paper, we propose a model, Sparse Structural Network Embedding (SSNE), to obtain node representation for link predication in sparse networks. The SSNE first transforms the adjacency matrix into the Sum of Normalized $H$-order Adjacency Matrix (SNHAM), and then maps the SNHAM matrix into a $d$-dimensional feature matrix for node representation via a neural network model. The mapping operation is proved to be an equivalent variation of singular value decomposition. Finally, we calculate nodal similarities for link prediction based on such feature matrix. By extensive testing experiments bases on synthetic and real sparse network, we show that the proposed method presents better link prediction performance in comparison of those of structural similarity indexes, matrix optimization and other graph embedding models.

中文翻译：

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SSNE：稀疏网络中链路预测的有效节点表示

图嵌入在复杂网络中的链接预测中越来越受欢迎，并获得了出色的性能。然而，在代表大多数真实网络的稀疏网络中已经完成了有限的工作。在本文中，我们提出了一个模型，稀疏结构网络嵌入（SSNE），以获得稀疏网络中链路预测的节点表示。SSNE首先将邻接矩阵转化为归一化$H$阶邻接矩阵之和（SNHAM），然后通过神经网络模型将SNHAM矩阵映射为$d$维特征矩阵用于节点表示。映射操作被证明是奇异值分解的等效变体。最后，我们根据这样的特征矩阵计算链路预测的节点相似度。通过基于合成和真实稀疏网络的大量测试实验，