Abstract
In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor \(N>>3\). To overcome this problem, we propose an efficient algorithm called TT-WOPT (Tensor-train Weighted OPTimization) to find the latent core tensors of tensor data and recover the missing entries. Tensor-train decomposition, which has the powerful representation ability with linear scalability to tensor order, is employed in our algorithm. The experimental results on synthetic data and natural image completion demonstrate that our method significantly outperforms the other related methods. Especially when the missing rate of data is very high, e.g., 85% to 99%, our algorithm can achieve much better performance than other state-of-the-art algorithms.
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Acknowledgments
This work is supported by JSPS KAKENHI (Grant No. 17K00326) and KAKENHI (Grant No. 15H04002).
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Yuan, L., Zhao, Q., Cao, J. (2017). Completion of High Order Tensor Data with Missing Entries via Tensor-Train Decomposition. In: Liu, D., Xie, S., Li, Y., Zhao, D., El-Alfy, ES. (eds) Neural Information Processing. ICONIP 2017. Lecture Notes in Computer Science(), vol 10634. Springer, Cham. https://doi.org/10.1007/978-3-319-70087-8_24
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DOI: https://doi.org/10.1007/978-3-319-70087-8_24
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