Adaptive Embedding for Temporal Network

Temporal network has become ubiquitous with the rise of online social platform and e-commerce, but largely under investigated in literature. In this paper, we propose a statistical framework for temporal network analysis, leveraging strengths of adaptive network merging, tensor decomposition and point process. A two-step embedding procedure and a regularized maximum likelihood estimate based on Poisson point process is developed, where the initial estimate is based on equal spaced time intervals while the final estimate on the adaptively merging time intervals. A projected gradient descent algorithm is proposed to facilitate estimation, where the upper bound of the tensor estimation error in each iteration is established. Through analysis, it is shown that the tensor estimation error is significantly reduced by the proposed method. Extensive numerical experiments also validate this phenomenon, as well as its advantage over other existing competitors. The proposed method is also applied to analyze a militarized interstate dispute dataset, where not only the prediction accuracy increases, but the adaptively merged intervals also lead to clear interpretation.