Temporal Network Prediction and Interpretation
Speaker: Huijuan Wang
Abstract: Communications networks such as opportunistic mobile networks, vehicle networks, and social contact networks can be represented as temporal networks, where two mobile devices (autos or individuals) are connected only when they are close to each other. These networks facilitate the propagation of information, epidemics and computer viruses. For example, epidemic spreads from one individual to another through time specific physical interactions. These networks are not static but temporal, i.e., evolving over time. Predicting temporal networks in the future and identifying the mechanisms that form temporal networks are crucial to effectively forecast and mitigate spreading processes. In this talk, I will introduce our methods for temporal network prediction: interpretable learning algorithms and network-based models (predict future network based on network properties of node pairs observed in the past). These methods enable not only relatively accurate network prediction but also the discovery of intrinsic network properties that facilitate network prediction and possible network formation mechanisms.
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Unrolling of Simplicial ElasticNet for Edge Flow Signal Reconstruction
Speaker: Chengen Liu
Abstract: The edge flow reconstruction task consists of retreiving edge flow signals from corrupted or incomplete measurements. This is typically solved by a regularized optimization problem on higher-order networks such as simplicial complexes and the corresponding regularizers are chosen based on prior knowledge. Tailoring this prior to the setting of interest can be challenging or it may not even be possible. Thus, we consider to learn this prior knowledge via a model-based deep learning approach. We propose a new regularized optimization problem for the simplicial edge flow reconstruction task, the simplicial ElasticNet, which combines the advantages of the L1 and L2 norms. We solve the simplicial ElasticNet problem via the multi-block alternating direction method of multipliers (ADMM) algorithm and provide conditions on its convergence. By unrolling the ADMM iterative steps, we develop a model-based neural network with a low requirement on the number of training data. This unrolling network replaces the fixed parameters in the iterative algorithm by learnable weights, thus exploiting the neural network’s learning capability while preserving the iterative algorithm’s interpretability. We enhance this unrolling network via simplicial convolutional filters to aggregate information from the edge flow neighbors, ultimately, improving the network learning expressivity. Extensive experiments on real-world and synthetic datasets validate the proposed approaches and show considerable improvements over both baselines and traditional non-model-based neural networks.
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Temporal-topological properties of higher-order evolving networks
Speaker: Alberto Ceria
Abstract: Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more than two people. Such group interactions can be represented as higher-order events of an evolving network. Here, we propose methods to characterize the temporal-topological properties of higher-order events to compare networks and identify their (dis)similarities. We analyzed 8 real-world physical contact networks, finding the following: (a) Events of different orders close in time tend to be also close in topology; (b) Nodes participating in many different groups (events) of a given order tend to involve in many different groups (events) of another order; Thus, individuals tend to be consistently active or inactive in events across orders; (c) Local events that are close in topology are correlated in time, supporting observation (a). Differently, in 5 collaboration networks, observation (a) is almost absent; Consistently, no evident temporal correlation of local events has been observed in collaboration networks. Such differences between the two classes of networks may be explained by the fact that physical contacts are proximity based, in contrast to collaboration networks. Our methods may facilitate the investigation of how properties of higher-order events affect dynamic processes unfolding on them and possibly inspire the development of more refined models of higher-order time-varying networks.
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