A multi-resolution approach to learning with overlapping communities

The recent few years have witnessed a rapid surge of par-ticipatory web and social media, enabling a new laboratory for studying human relations and collective behavior on an unprecedented scale. In this work, we attempt to harness the predictive power of social connections to determine the preferences or behaviors of individuals such as whether a user supports a certain political view, whether one likes one product, whether he/she would like to vote for a presidential candidate, etc. Since an actor is likely to participate in mul-tiple different communities with each regulating the actor’s behavior in varying degrees, and a natural hierarchy might exist between these communities, we propose to zoom into a network at multiple different resolutions and determine which communities are informative of a targeted behavior. We develop an efficient algorithm to extract a hierarchy of overlapping communities. Empirical results on several large-scale social media networks demonstrate the superiority of our proposed approach over existing ones without consider-ing the multi-resolution or overlapping property, indicating its highly promising potential in real-world applications

Detecting the community structure and activity patterns of temporal networks: a non-negative tensor factorization approach

The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule