Abstract
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 the tensor analog that attempts to impute missing tensor entries from similar low-rank type assumptions. In this paper, we study the tensor completion problem when the sampling pattern is deterministic and possibly non-uniform. We first propose an efficient weighted Higher Order Singular Value Decomposition (HOSVD) algorithm for the recovery of the underlying low-rank tensor from noisy observations and then derive the error bounds under a properly weighted metric. Additionally, the efficiency and accuracy of our algorithm are both tested using synthetic and real datasets in numerical simulations.
Highlights
In many data-rich domains such as computer vision, neuroscience, and social networks, tensors have emerged as a powerful paradigm for handling the data deluge
We propose a simple but efficient algorithm named the weighted Higher Order Singular Value Decomposition (HOSVD)
The efficiency of our proposed weighted HOSVD algorithm is shown by numerical simulations
Summary
In many data-rich domains such as computer vision, neuroscience, and social networks, tensors have emerged as a powerful paradigm for handling the data deluge. As caused by various unpredictable or unavoidable reasons, multidimensional datasets are commonly raw and incomplete, and often only a small subset of entries of tensors are available. It is, natural to address the above issue using tensor completion in modern data-driven applications, in which data are naturally represented as a tensor, such as image/video inpainting [5,8], link-prediction [9], and recommendation systems [10], to name a few
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