Laetitia Gauvin

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.

Activity clocks: spreading dynamics on temporal networks of human contact

Dynamical processes on time-varying complex networks are key to understanding and modeling a broad variety of processes in socio-technical systems. Here we focus on empirical temporal networks of human proximity and we aim at understanding the factors that, in simulation, shape the arrival time distribution of simple spreading processes. Abandoning the notion of wall-clock time in favour of node-specific clocks based on activity exposes robust statistical patterns in the arrival times across different social contexts. Using randomization strategies and generative models constrained by data, we show that these patterns can be understood in terms of heterogeneous inter-event time distributions coupled with heterogeneous numbers of events per edge. We also show, both empirically and by using a synthetic dataset, that significant deviations from the above behavior can be caused by the presence of edge classes with strong activity correlations.

Detecting Anomalies in Time-Varying Networks Using Tensor Decomposition

New data sources from sensor networks and Internet-of-Things applications promise a wealth of interaction data that can be naturally represented as time-varying networks. This brings forth new challenges for the identification and removal of time-varying graph anomalies that entail complex correlations of topological features and temporal activity patterns. Here we present an anomaly detection approach for temporal graph data, based on an iterative tensor decomposition and masking procedure. We test this approach using high-resolution social network data from wearable proximity sensors. The dataset includes metadata that allow to independently build a ground truth, used to validate the anomaly detection method. Our approach achieves high accuracy in identifying meso-scale network anomalies due to sensor wearing protocol, proving the practical viability of the method for a real-world application.

Fingerprinting temporal networks of close-range human proximity

Mobile devices and wearable sensors are making available records of human mobility and proximity with unprecedented levels of detail. Here we focus on close-range human proximity networks measured by means of wireless wearable sensors in a variety of real-world environments. We show that simple dynamical processes computed over the time-varying proximity networks can uncover important features of the interaction patterns that go beyond standard statistical indicators of heterogeneity and burstiness, and can tell apart datasets that would otherwise look statistically similar. We show that, due to the intrinsic temporal heterogeneity of human dynamics, the characterization of spreading processes over time-varying networks of human contact may benefit from abandoning the notion of wall-clock time in favor of a node-specific notion of time based on the contact activity of individual nodes.

Change points, memory and epidemic spreading in temporal networks

Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks attempt to capture only a single characteristic time scale in isolation — typically associated with the short-time memory of a Markov chain or with long-time abrupt changes caused by external or systemic events. Here we propose a unified approach to model both aspects simultaneously, detecting short and long-time behaviors of temporal networks. We do so by developing an arbitrary-order mixed Markov model with change points, and using a nonparametric Bayesian formulation that allows the Markov order and the position of change points to be determined from data without overfitting. In addition, we evaluate the quality of the multiscale model in its capacity to reproduce the spreading of epidemics on the temporal network, and we show that describing multiple time scales simultaneously has a synergistic effect, where statistically significant features are uncovered that otherwise would remain hidden by treating each time scale independently.