iFCTN: an intra-block Fully-Connected Tensor Network Decomposition for Tensor Completion

The fully-connected tensor network (FCTN) decomposition has recently exhibited strong modeling capabilities by connecting every pair of tensor factors, thereby capturing rich cross-mode correlations. However, this advantage comes with an inherent limitation: updating the factors typically requires reconstructing auxiliary sub-networks, which entails extensive and cumbersome (un)folding. In this study, we propose the intra-block FCTN (iFCTN) decomposition, a novel (un)folding-free variant of FCTN decomposition designed to enhance computational efficiency. We parameterize each FCTN factor through Khatri-Rao products, which significantly reduces the complexity of reconstructing intermediate sub-networks and yields subproblems with well-structured coefficient matrices. Furthermore, we deploy the proposed iFCTN decomposition on the representative task of tensor completion and design an efficient proximal alternating minimization algorithm. Theoretically, we establish its global convergence to a critical point. Extensive experiments demonstrate that iFCTN outperforms state-of-the-art methods with a lower computational overhead.