Discrete mathematics

Physics

Macro

Mathematics

Operating system

Network dynamics

Dynamics (music)

Artificial intelligence

Acoustics

Programming language

Computer science

Quantum mechanics

Theoretical computer science

Process (computing)

Embedding

Node (physics)

Network embedding aims to embed nodes into a low-dimensional space, while capturing the network structures and properties. Although quite a few promising network embedding methods have been proposed, most of them focus on static networks. In fact, temporal networks, which usually evolve over time in terms of microscopic and macroscopic dynamics, are ubiquitous. The micro-dynamics describe the formation process of network structures in a detailed manner, while the macro-dynamics refer to the evolution pattern of the network scale. Both micro- and macro-dynamics are the key factors to network evolution; however, how to elegantly capture both of them for temporal network embedding, especially macro-dynamics, has not yet been well studied. In this paper, we propose a novel temporal network embedding method with micro- and macro-dynamics, named $\rmM^2DNE $. Specifically, for micro-dynamics, we regard the establishments of edges as the occurrences of chronological events and propose a temporal attention point process to capture the formation process of network structures in a fine-grained manner. For macro-dynamics, we define a general dynamics equation parameterized with network embeddings to capture the inherent evolution pattern and impose constraints in a higher structural level on network embeddings. Mutual evolutions of micro- and macro-dynamics in a temporal network alternately affect the process of learning node embeddings. Extensive experiments on three real-world temporal networks demonstrate that $\rmM^2DNE $ significantly outperforms the state-of-the-arts not only in traditional tasks, e.g., network reconstruction, but also in temporal tendency-related tasks, e.g., scale prediction.

Temporal Network Embedding with Micro- and Macro-dynamics