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In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train Optimization (STTO) which considers incomplete data as sparse tensor and uses first-order optimization method to find the factors of tensor-train decomposition. Our algorithm is shown to perform well in simulation experiments at both low-order cases and high-order cases.
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