Detecting and Tracking Community Structure in Temporal Networks: A Low-Rank + Sparse Estimation Based Evolutionary Clustering Approach

Networks provide a powerful tool to model complex systems where the different entities in the system are presented by nodes and their interactions by edges. With the availability of network-type data, different community detection algorithms have been proposed to investigate the organization of the nodes within these networks. In particular, numerous graph-based community detection algorithms have been developed for static networks. However, most real complex systems vary with time. Consequently, it is important to develop graph-based community detection techniques for temporal networks. In this paper, a new low-rank + sparse estimation based evolutionary spectral clustering approach is proposed to detect and track the community structure in temporal networks. The proposed method decomposes the network into low-rank and sparse parts and obtains smooth cluster assignments by minimizing the subspace distance between consecutive time points. The extracted low-rank adjacency matrix is then used for clustering and the subspaces are defined through spectral embedding. The introduced framework is robust to noise and outliers and can detect the community structure in both binary and weighted temporal networks efficiently without making any prior assumptions about the network structure. The proposed approach is evaluated on several weighted and binary simulated and real temporal networks. The results show that the proposed algorithm can detect and track the correct community structure over time efficiently and outperforms state-of-the-art algorithms.