Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion

The popular tensor train (TT) and ring (TR) decompositions have achieved promising results in science engineering. However, TT TR only establish an operation between adjacent two factors are highly sensitive to the permutation of modes, leading inadequate inflexible representation. In this paper, we propose a generalized decomposition, which decomposes Nth-order into set establishes any factors. Since it can be graphically interpreted as fully-connected network, named network (FCTN) decomposition. superiorities FCTN decomposition lie outstanding capability for characterizing adequately intrinsic correlations modes tensors essential invariance transposition. Furthermore, employ one representative task, i.e., completion, develop efficient solving algorithm based on proximal alternating minimization. Theoretically, prove convergence developed algorithm, sequence obtained by globally converges critical point. Experimental substantiate that proposed method compares favorably state-of-the-art methods other decompositions.