Temporally Factorized Network Modeling for Evolutionary Network Analysis

TLDR: This work shows that it is indeed possible to achieve the goal of representing the edge structure of the network purely as a function of time with the use of a matrix factorization, in which the entries are parameterized by time.

Abstract: The problem of evolutionary network analysis has gained increasing attention in recent years, because of an increasing number of networks, which are encountered in temporal settings. For example, social networks, communication networks, and information networks continuously evolve over time, and it is desirable to learn interesting trends about how the network structure evolves over time, and in terms of other interesting trends. One challenging aspect of networks is that they are inherently resistant to parametric modeling, which allows us to truly express the edges in the network as functions of time. This is because, unlike multidimensional data, the edges in the network reflect interactions among nodes, and it is difficult to independently model the edge as a function of time, without taking into account its correlations and interactions with neighboring edges. Fortunately, we show that it is indeed possible to achieve this goal with the use of a matrix factorization, in which the entries are parameterized by time. This approach allows us to represent the edge structure of the network purely as a function of time, and predict the evolution of the network over time. This opens the possibility of using the approach for a wide variety of temporal network analysis problems, such as predicting future trends in structures, predicting links, and node-centric anomaly/event detection. This flexibility is because of the general way in which the approach allows us to express the structure of the network as a function of time. We present a number of experimental results on a number of temporal data sets showing the effectiveness of the approach.