Robust Tensor Completion with Side Information

Although robust tensor completion has been extensively studied, the effect of incorporating side information has not been explored. In this article, we fill this gap by developing a novel higher-order robust tensor completion model that incorporates both latent and explicit side information. We base our model on the transformed t-product because the corresponding tensor tubal rank can characterize the inherent low-rank structure of a tensor. We study the effect of side information on sample complexity and prove that our model needs fewer observations than other tensor recovery methods when side information is perfect. This theoretically shows that informative side information is beneficial for learning. Extensive experimental results on synthetic and real data further demonstrate the superiority of the proposed method over several popular alternatives. In particular, we consider link prediction in signed networks and rating prediction in recommender systems. We show that the proposed model yields better results than other methods in the learning of such low-rank tensor data because it can better exploit side information in learning