Predicting and Interpreting Bipartite Temporal Networks

Abstract

A network, is defined as a collection of nodes interconnected by links. When this topology changes through time, we call it a temporal network. A specific class of networks, with only two types of nodes with no connections between one kind, is the bipartite network. An example is a telecommunications network, where nodes represent telecommunication base station and various mobile services like web-browsing, streaming etc. A link may exist only between a base station and a service. Moreover, each link is associated with a time-evolving weight, which represents the volume of the traffic between the corresponding base station and service over time. This weight associated with each link is also called the activity weight, with the link considered active only when the weight is non-zero. Predicting such a temporal weighted network in the future is crucial for telecommunications engineers, allowing for e.g., better traffic management. Prediction of the unweighted temporal network one step ahead, at time $t+1$, based on the network observed in the past between $[t-L-1; t]$, has been studied recently in contact networks. However, the prediction of weighted temporal networks, or equivalently, predicting the activity weight of each link, in the future has not been explored yet. Moreover, we also aim to uncover the mechanisms that enable the prediction of a weighted temporal network. We achieve this by devising several strategies that help us select the most relevant links within the network, whose activity weights in the past serve as the input for the interpretable, statistical learning algorithm, LASSO Regression, to predict the activity of a given target link at time $t+1$. The focus of the strategies is to capture a relationship of activity weights between the selected and target links. These selected links range from most active links (amount of timesteps the link weight is non-zero), those with largest activity weights or most similar to the target link using several metrics. In this thesis we apply this general methodology to two bipartite networks sourced from real world data and evaluate the performance of different strategies. Through the learned LASSO coefficients and prediction accuracy, we discover that past activity weight of a link is the best predictor for it's future weights. In terms of predicting power, most is coming from the past weights of the link we want to predict and one or two neighbouring links. Most of the selected links have minimal impact on the prediction accuracy. While different strategies of link selection excel in specific conditions, their improvement over the random link selection, is relatively low. The proposed method could be further applied to predict other weighted temporal networks with different properties to understand whether and how the the performance of link selection strategies depends on properties of the network to be predicted.