High-order Proximity Preserved Embedding For Dynamic Networks

Network embedding, aiming to embed a network into a low dimensional vector space while preserving the inherent structural properties of the network, has attracted considerable attention. However, most existing embedding methods focus on the static network while neglecting the evolving characteristic of real-world networks. Meanwhile, most of previous methods cannot well preserve the high-order proximity, which is a critical structural property of networks. These problems motivate us to seek an effective and efficient way to preserve the high-order proximity in embedding vectors when the networks evolve over time. In this paper, we propose a novel method of Dynamic High-order Proximity preserved Embedding (DHPE). Specifically, we adopt the generalized SVD (GSVD) to preserve the high-order proximity. Then, by transforming the GSVD problem to a generalized eigenvalue problem, we propose a generalized eigen perturbation to incrementally update the results of GSVD to incorporate the changes of dynamic networks. Further, we propose an accelerated solution to the DHPE model so that it achieves a linear time complexity with respect to the number of nodes and number of changed edges in the network. Our empirical experiments on one synthetic network and several real-world networks demonstrate the effectiveness and efficiency of the proposed method.