A robust tensor completion method integrating matrix factorization and fully-connected tensor network decomposition

The fully-connected tensor network (FCTN) decomposition has attracted significant attention due to its novel structure and superior performance. However, the effectiveness of this type of method heavily depends on the choice of initial ranks. To address this issue, the Frobenius norm constraint is introduced to FCTN factor tensor to promote the low-rank property of the target tensor. As a result, the proposed method remains robust even when the initial ranks are improperly set. To solve the resulting non-convex optimization problem, a proximal alternating minimization algorithm is designed. Extensive experiments on both synthetic and real-world data demonstrate that the proposed method not only outperforms several state-of-the-art tensor decomposition approaches but also exhibits significantly less sensitivity to the choice of initial ranks compared to existing FCTN-based methods.