In recent years, network embedding has attracted extensive interests, which aims at representing nodes of an original network in a low-dimensional vector space while preserving the inherent topological structures of the network. Despite the remarkable advantages of complex networks, most existing network embedding methods are mainly focused on static networks while ignoring the evolving characteristic, which is proved to be an essential property of real-world networks. In this paper, we propose Node Proximity Preserved Dynamic Network Embedding via Matrix Perturbation (NPDNE) to tackle the dilemma. Specifically, our method implements a low-rank transformation on the normalized Laplacian matrix of the given networks and then derives the embedding vectors through generalized SVD. Subsequently, the node proximities are preserved in the embedding vectors by exploiting the eigen-decomposition reweighing theorem, which reveals the intrinsic relationship among different-order proximities. Moreover, a generalized eigen perturbation is adopted to update the embedding vectors so that the evolution of given networks can be captured over time. Finally, we conduct experiments of multi-label classification, link prediction, and visualization on several real-world datasets. The experimental results demonstrate the superiority of the proposed NPDNE model compared with state-of-the-art baselines.

近年来，网络嵌入引起了广泛的兴趣，其目的是在保留低维向量空间的同时保留网络固有的拓扑结构的同时表示原始网络的节点。尽管复杂网络具有显着的优势，但是大多数现有的网络嵌入方法主要集中在静态网络上，而忽略了其不断发展的特性，这被证明是现实世界网络的基本特性。在本文中，我们提出了通过矩阵扰动（NPDNE）保留节点邻近度的动态网络嵌入来解决这一难题。具体来说，我们的方法在给定网络的规范化Laplacian矩阵上实现了低秩变换，然后通过广义SVD推导了嵌入向量。后来，利用特征分解重称定理，将节点的邻近点保留在嵌入向量中，揭示了不同阶邻近点之间的内在联系。此外，采用广义特征扰动来更新嵌入矢量，以便可以随时间捕获给定网络的演化。最后，我们在多个真实数据集上进行了多标签分类，链接预测和可视化的实验。实验结果证明了所提出的NPDNE模型与最新基线相比的优越性。采用广义特征扰动来更新嵌入向量，以便可以随时间捕获给定网络的演化。最后，我们在多个真实数据集上进行了多标签分类，链接预测和可视化的实验。实验结果证明了所提出的NPDNE模型与最新基线相比的优越性。采用广义特征扰动来更新嵌入向量，以便可以随时间捕获给定网络的演化。最后，我们在多个真实数据集上进行了多标签分类，链接预测和可视化的实验。实验结果证明了所提出的NPDNE模型与最新基线相比的优越性。