Regularized matrix completion with partial side information

Side information has been shown useful for improving the performance of matrix completion applications. However, in most cases, only partial side information of either the column or row space is available. In this work, we propose a novel regularization based model to incorporate partial side information in matrix completion. We provide theoretical guarantees to ensure the success of the proposed model. It is proved that the proposed model achieves the state-of-the-art sample complexity when the given partial side information is exact, and an error bound for inexact partial side information is also provided. Moreover, we provide a deterministic rule for the selection of regularization parameter. We conduct extensive experiments on both synthetic and real-world data-sets. Experimental results show that our model succeeds to incorporate partial side information, and outperforms the state-of-the-art models on most data-sets.