Network representation learning, as an approach to learn low dimensional representations of vertices, has attracted considerable research attention recently. It has been proven extremely useful in many machine learning tasks over large graph. Most existing methods focus on learning the structural representations of vertices in a static network, but cannot guarantee an accurate and efficient embedding in a dynamic network scenario. The fundamental problem of continuously capturing the dynamic properties in an efficient way for a dynamic network remains unsolved. To address this issue, we present an efficient incremental skip-gram algorithm with negative sampling for dynamic network embedding, and provide a set of theoretical analyses to characterize the performance guarantee. Specifically, we first partition a dynamic network into the updated, including addition/deletion of links and vertices, and the retained networks over time. Then we factorize the objective function of network embedding into the added, vanished and retained parts of the network. Next we provide a new stochastic gradient-based method, guided by the partitions of the network, to update the nodes and the parameter vectors. The proposed algorithm is proven to yield an objective function value with a bounded difference to that of the original objective function. The first order moment of the objective difference converges in order of \(\mathbb{O}(\frac{1}{n^{2}})\), and the second order moment of the objective difference can be stabilized in order of \(\mathbb{O}(1)\). Experimental results show that our proposal can significantly reduce the training time while preserving the comparable performance. We also demonstrate the correctness of the theoretical analysis and the practical usefulness of the dynamic network embedding. We perform extensive experiments on multiple real-world large network datasets over multi-label classification and link prediction tasks to evaluate the effectiveness and efficiency of the proposed framework, and up to 22 times speedup has been achieved.

网络表示学习作为一种学习顶点的低维表示的方法，最近引起了相当大的研究关注。它已被证明在大型图上的许多机器学习任务中极为有用。现有的大多数方法都专注于学习静态网络中顶点的结构表示，但不能保证在动态网络场景中准确有效地嵌入。仍然没有解决以有效方式连续捕获动态网络的动态属性的基本问题。为了解决这个问题，我们提出了一种有效的增量式跳过文法算法，该算法具有用于动态网络嵌入的负采样，并提供了一组理论分析来表征性能保证。具体来说，我们首先将动态网络划分为更新后的网络，包括添加/删除链接和顶点，以及随着时间的推移保留的网络。然后，我们将网络嵌入的目标函数分解为网络的添加部分，消失部分和保留部分。接下来，我们在网络分区的指导下，提供了一种新的基于随机梯度的方法来更新节点和参数向量。实践证明，所提出的算法能够产生与原始目标函数有一定差异的目标函数值。客观差的一阶矩收敛于 在网络分区的引导下，更新节点和参数向量。实践证明，所提出的算法能够产生与原始目标函数有一定差异的目标函数值。客观差的一阶矩收敛于 在网络分区的引导下，更新节点和参数向量。实践证明，所提出的算法能够产生与原始目标函数有一定差异的目标函数值。客观差的一阶矩收敛于\（\ mathbb {O}（\ frac {1} {n ^ {2}}）\），可以按\（\ mathbb {O}（1）\ ）。实验结果表明，我们的建议可以显着减少训练时间，同时保持可比的性能。我们还证明了理论分析的正确性和动态网络嵌入的实用性。我们通过多标签分类和链接预测任务对多个真实世界的大型网络数据集进行了广泛的实验，以评估所提出框架的有效性和效率，并且实现了高达22倍的加速。