Low-Complexity Hyperbolic Embedding Schemes for Temporal Complex Networks

Abstract

Hyperbolic embedding can effectively preserve the property of complex networks. Though some state-of-the-art hyperbolic node embedding approaches are proposed, most of them are still not well suited for the dynamic evolution process of temporal complex networks. The complexities of the adaptability and embedding update to the scale of complex networks with moderate variation are still challenging problems. To tackle the challenges, we propose hyperbolic embedding schemes for the temporal complex network within two dynamic evolution processes. First, we propose a low-complexity hyperbolic embedding scheme by using matrix perturbation, which is well-suitable for medium-scale complex networks with evolving temporal characteristics. Next, we construct the geometric initialization by merging nodes within the hyperbolic circular domain. To realize fast initialization for a large-scale network, an R tree is used to search the nodes to narrow down the search range. Our evaluations are implemented for both synthetic networks and realistic networks within different downstream applications. The results show that our hyperbolic embedding schemes have low complexity and are adaptable to networks with different scales for different downstream tasks.