Network embedding is a technique used to generate low-dimensional vectors representing each node in a network while maintaining the original topology and properties of the network. This technology enables a wide range of learning tasks, including node classification and link prediction. However, the current landscape of network embedding approaches predominantly revolves around static networks, neglecting the dynamic nature that characterizes real social networks. Dynamics at both the micro- and macrolevels are fundamental drivers of network evolution. Microlevel dynamics provide a detailed account of the network topology formation process, while macrolevel dynamics reveal the evolutionary trends of the network. Despite recent dynamic network embedding efforts, a few approaches accurately capture the evolution patterns of nodes at the microlevel or effectively preserve the crucial dynamics of both layers. Our study introduces a novel method for embedding networks, i.e., bilayer evolutionary pattern-preserving embedding for dynamic networks (Bi-DNE), that preserves the evolutionary patterns at both the micro- and macrolevels. The model utilizes strengthened triadic closure to represent the network structure formation process at the microlevel, while a dynamic equation constrains the network structure to adhere to the densification power-law evolution pattern at the macrolevel. The proposed Bi-DNE model exhibits significant performance improvements across a range of tasks, including link prediction, reconstruction, and temporal link analysis. These improvements are demonstrated through comprehensive experiments carried out on both simulated and real-world dynamic network datasets. The consistently superior results to those of the state-of-the-art methods provide empirical evidence for the effectiveness of Bi-DNE in capturing complex evolutionary patterns and learning high-quality node representations. These findings validate the methodological innovations presented in this work and mark valuable progress in the emerging field of dynamic network representation learning. Further exploration demonstrates that Bi-DNE is sensitive to the analysis task parameters, leading to a more accurate representation of the natural evolution process during dynamic network embedding.
