High-order Tensor Completion for Data Recovery via Sparse Tensor-train Optimization
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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 performance and tensor order linear scalability. We propose an algorithm named STTO (Sparse Tensor-train Optimization) 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. We also employ a tensorization method to transform data to a higher-order to enhance the performance of our algorithm. The image recovery experiment results in various cases manifest that our method outperforms other completion algorithms. Especially when the missing rate is very high, e.g. 90 performance than other state-of-the-art methods.
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