HOSVD-Based Algorithm for Weighted Tensor Completion

Matrix completion, the problem of completing missing entries in a data matrix with low-dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is tensor analog that attempts to impute from similar low-rank type assumptions. In this paper, we study when sampling pattern deterministic possibly non-uniform. We first propose an efficient weighted Higher Order Singular Value Decomposition (HOSVD) algorithm for recovery underlying noisy observations then derive error bounds under properly metric. Additionally, efficiency accuracy our are both tested using synthetic real datasets numerical simulations.