LAUSR

Structural network analysis, including node ranking, community detection, and link prediction, has received a lot of attention lately. In the literature, most works focused on the structural analysis of a single network. In this paper, we are particularly interested in how the network structure evolves over time. For this, we propose a general framework to track, model, and predict the dynamic network structures. Unlike some recent works that directly tracks the adjacency matrices of the networks, our framework utilizes the spectral graph theory to track the latent feature vectors obtained by a low-rank eigendecomposition of the Laplacian matrices of the networks. We then use the Finite Impulse Response (FIR) filter to model the evolution of the latent feature vector of each node. By solving a ridge regression problem, the parameters of the FIR filter can be learned and used for predicting the future network structures, including node ranking, community detection, and link prediction. To test the effectiveness of our framework, we perform various experiments based on our synthetic datasets and three real-world datasets. Our experimental results show that our framework is very effective in tracking latent feature vectors and predicting future network structures.