Revealing latent factors of temporal networks for mesoscale intervention in epidemic spread

The customary perspective to reason about epidemic mitigation in temporal networks hinges on the identification of nodes with specific features or network roles. The ensuing individual-based control strategies, however, are difficult to carry out in practice and ignore important correlations between topological and temporal patterns. Here we adopt a mesoscopic perspective and present a principled framework to identify collective features at multiple scales and rank their importance for epidemic spread. We use tensor decomposition techniques to build an additive representation of a temporal network in terms of mesostructures, such as cohesive clusters and temporally-localized mixing patterns. This representation allows to determine the impact of individual mesostructures on epidemic spread and to assess the effect of targeted interventions that remove chosen structures. We illustrate this approach using high-resolution social network data on face-to-face interactions in a school and show that our method affords the design of effective mesoscale interventions.

Mining Concurrent Topical Activity in Microblog Streams

Streams of user-generated content in social media exhibit patterns of collective attention across diverse topics, with temporal structures determined both by exogenous factors and endogenous factors. Teasing apart different topics and resolving their individual, concurrent, activity timelines is a key challenge in extracting knowledge from microblog streams. Facing this challenge requires the use of methods that expose latent signals by using term correlations across posts and over time. Here we focus on content posted to Twitter during the London 2012 Olympics, for which a detailed schedule of events is independently available and can be used for reference. We mine the temporal structure of topical activity by using two methods based on non-negative matrix factorization. We show that for events in the Olympics schedule that can be semantically matched to Twitter topics, the extracted Twitter activity timeline closely matches the known timeline from the schedule. Our results show that, given appropriate techniques to detect latent signals, Twitter can be used as a social sensor to extract topical-temporal information on real-world events at high temporal resolution.

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.