Detecting the Community Structure and Activity Patterns of Temporal Networks: A Non-Negative Tensor Factorization Approach

Abstract

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.

Non-Negative Tensor Factorization for Human Behavioral Pattern Mining in Online Games

“…However, due to their multiple dimensions, tensors are suitable objects to represent multimodal data [25]. This allows to identify correlation in the data at different levels [26]: on the one hand, the application of the NTF helps in the identification of hidden topological structures in the data, like groups or communities, which are easy to interpret as they reflect individuals' social dynamics [27]. On the other hand, these topological structures share correlated activity patterns [28,29].…”

Exploring Twitter communication dynamics with evolving community analysis

“…Real-world OSNs, however, are definitely not static. The networks formed in services such as Twitter undergo major and rapid changes over time, which places them in the field of dynamic networks (Asur, Parthasarathy & Ucar, 2007;Palla, Barabasi & Vicsek, 2007;Takaffoli et al, 2011;Tantipathananandh, Berger-Wolf & Kempe, 2007;Roy Chowdhury & Sukumar, 2014;Gauvin, Panisson & Cattuto, 2014;Greene, Doyle & Cunningham, 2010;Aktunc et al, 2015;Albano, Guillaume & Le Grand, 2014). These changes are manifested as users join in or leave one or more communities, by friends mentioning each other to attract attention or by new users referencing a total stranger.…”

“…A dynamic community is formed by a temporal array of the aforementioned communities with the condition that they share common users (Cazabet & Amblard, 2014;Nguyen et al, 2014). Community evolution detection has been previously used to study the temporal structure of a network (Gauvin, Panisson & Cattuto, 2014;Greene, Doyle & Cunningham, 2010;Palla, Barabasi & Vicsek, 2007;Takaffoli et al, 2011). However, even by establishing only the communities that sustain interest over time, the amount of communities and thus metadata that a user has to scan through is immense.…”

Evolution properties of the community members for dynamic networks

“…Asur et al [19] developed a framework for capturing and identifying community events which are used to characterize complex behavioral patterns of individuals and communities over time. Gauvin et al [20] used the non-negative tensor factorization method to extract the community activities of dynamic networks. Wang [21] found that community merging depends largely on the clustering coefficient of the nodes connecting two communities directly, while community splitting depends on the clustering coefficient of the nodes in the community for social networks.…”