Tensor completion via multi-shared-modes canonical correlation analysis

Low-rank tensor completion (LRTC) has been applied in many real-world problems. But most of the existing LRTC methods recover a tensor on a single dataset with the low-rank assumption, suffering from a low accuracy due to the complicated structures of higher-order data. To address this issue, we propose a novel tensor completion method for two correlated tensor datasets obtained from different sources. We first introduce the correlated tensors with multiple shared modes via tensor canonical correlation analysis (TCCA), and reveal the relationship between the transformation matrices of TCCA and the Tucker decomposition. Then we develop a Tucker-n decomposition method with n invariant modes to capture the latent structures of incomplete tensors, in which sufficient discriminative information for TCCA can be flexibly maintained by varying the number of invariant modes. Finally, we combine the Tucker-n decomposition method for LRTC with the correlation of TCCA as a regularizer to improve the completion performance, and derive relative error bounds for our LRTC approach to guarantee the recovery accuracy. Experimental results on synthetic and real data demonstrate the accuracy and efficiency of the proposed approach, as well as the benefit of multiple shared modes.