Networks have become indispensable and ubiquitous structures in many fields to model the interactions among different entities, such as friendship in social networks or protein interactions in biological graphs. A major challenge is to understand the structure and dynamics of these systems. Although networks evolve through time, most existing graph representation learning methods target only static networks. Whereas approaches have been developed for the modeling of dynamic networks, there is a lack of efficient continuous time dynamic graph representation learning methods that can provide accurate network characterization and visualization in low dimensions while explicitly accounting for prominent network characteristics such as homophily and transitivity. In this paper, we propose the Piecewise-Velocity Model (PiVeM) for the representation of continuous-time dynamic networks. It learns dynamic embeddings in which the temporal evolution of nodes is approximated by piecewise linear interpolations based on a latent distance model with piecewise constant node-specific velocities. The model allows for analytically tractable expressions of the associated Poisson process likelihood with scalable inference invariant to the number of events. We further impose a scalable Kronecker structured Gaussian Process prior to the dynamics accounting for community structure, temporal smoothness, and disentangled (uncorrelated) latent embedding dimensions optimally learned to characterize the network dynamics. We show that PiVeM can successfully represent network structure and dynamics in ultra-low two-dimensional spaces. It outperforms relevant state-of-art methods in downstream tasks such as link prediction. In summary, PiVeM enables easily interpretable dynamic network visualizations and characterizations that can further improve our understanding of the intrinsic dynamics of time-evolving networks.
翻译:在许多领域,网络已成为不可或缺的、无处不在的结构,可以模拟不同实体之间的相互作用,例如社交网络中的友谊或生物图形中的蛋白质互动。一个重大挑战是理解这些系统的结构和动态。虽然网络会随着时间演变,但大多数现有的图形代表学习方法只针对静态网络。虽然为动态网络建模开发了方法,但缺乏高效的连续时间动态代表学习方法,这些方法可以在低维层面提供准确的时间动态描述和可视化网络特征,同时明确考虑到显著的网络特征,例如可容易同性和中转性。在本文中,我们建议为连续时间动态网络的表示而采用平时流模型(PiViVeMeMeMeM) 模型。我们进一步将可伸缩的Krenter-Ve-Velity 模型的内向性动态解释,将节流网络的时空结构化网络的图性变化图解,以平流模式的形式显示我们之前的平流网络的平流模式。该模型允许以可伸缩的方式表达相关的Poissonson进程, 和可伸缩的精确地推导到事件数量。我们进一步把可伸缩的流- kreval-cle-deal-deal-deal-deal-deal-commal-deal-destral-deal-commal-commal-commal-commal-deal-deal-cal-c-cal-cal-c-cal-cal-c-c-c-c-cal-cal-calvicalvical-destr-cal-cal-cal-cal-cal-cil-cumental-cil-destr-cal-cal-sal-sal-sal-sal-sal-sal-sal-cal-cal-cal-cal-cal-cal-cal-cal-cal-mostral-mostral-mostral-cal-cal-mostral-cal-mostral-sal-sal-sal-sal-mocal-mocal-mostral-mocal-mocal-mocal-cal