  Coupled tensor decomposition reveals the joint data structure by
incorporating priori knowledge that come from the latent coupled factors. The
tensor ring (TR) decomposition is invariant under the permutation of tensors
with different mode properties, which ensures the uniformity of decomposed
factors and mode attributes. The TR has powerful expression ability and
achieves success in some multi-dimensional data processing applications. To let
coupled tensors help each other for missing component estimation, in this paper
we utilize TR for coupled completion by sharing parts of the latent factors.
The optimization model for coupled TR completion is developed with a novel
Frobenius norm. 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-art methods in terms of recovery accuracy.
