Low Rank Coupled Tensor Ring Completion

Coupled tensor decomposition can reveal the latent data structure with shared factors. In this paper, because of its outstanding performance in some multi-way data processing applications, the tensor ring is used for coupled tensor decomposition by sharing parts of the tensor ring factors of two coupled tensors. The corresponding optimization model for low rank coupled tensor ring completion is developed to let two tensors help each other for missing component estimation effectively. It is solved by the block coordinate descent algorithm which efficiently solves a series of quadratic problems resulted from sampling pattern. The excess risk bound for this optimization model shows the theoretical performance enhancement in comparison with other coupled nuclear norm based methods. The proposed method is validated on numerical experiments on synthetic data, and experimental results on real-world data demonstrate its superiority over the state-of-the-arts methods in terms of recovery accuracy.