Tensor reconstruction = Tensor completion and recovery
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Cichocki, Andrzej. "Era of big data processing: A new approach via tensor networks and tensor decompositions." arXiv preprint arXiv:1403.2048 (2014).(Paper)
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First definition of tensor nuclear norm, and transformation of tensor completion into a convex problem
Liu, Ji, et al. "Tensor completion for estimating missing values in visual data." IEEE transactions on pattern analysis and machine intelligence 35.1 (2012): 208-220.(Paper) (Code)
Gandy, Silvia, Benjamin Recht, and Isao Yamada. "Tensor completion and low-n-rank tensor recovery via convex optimization." Inverse Problems 27.2 (2011): 025010. (Paper)
Trace norm of square matrix reshape of tensor Theoritically more suitable for high dimensional tensor
Mu, Cun, et al. "Square deal: Lower bounds and improved relaxations for tensor recovery." International conference on machine learning. 2014. (Paper)
Acar, Evrim, et al. "Scalable tensor factorizations for incomplete data." Chemometrics and Intelligent Laboratory Systems 106.1 (2011): 41-56.(Paper) (Code)- It has been a function of tensor toolbox
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Chen, Yi-Lei, Chiou-Ting Hsu, and Hong-Yuan Mark Liao. "Simultaneous tensor decomposition and completion using factor priors." IEEE transactions on pattern analysis and machine intelligence 36.3 (2013): 577-591. (Paper) (Code)-supplementary material
Zhao, Qibin, Liqing Zhang, and Andrzej Cichocki. "Bayesian CP factorization of incomplete tensors with automatic rank determination." IEEE transactions on pattern analysis and machine intelligence 37.9 (2015): 1751-1763. (Paper) (Code)
Yokota, Tatsuya, Qibin Zhao, and Andrzej Cichocki. "Smooth PARAFAC decomposition for tensor completion." IEEE Transactions on Signal Processing 64.20 (2016): 5423-5436.(Paper) (Code)
Wu, Y., Tan, H., Li, Y., Zhang, J., & Chen, X. (2018). A fused CP factorization method for incomplete tensors. IEEE transactions on neural networks and learning systems, 30(3), 751-764. (Nonnegative factorization Code)
Zhang, L., Wei, W., Shi, Q., Shen, C., Hengel, A. V. D., & Zhang, Y. (2017). Beyond low rank: A data-adaptive tensor completion method. arXiv preprint arXiv:1708.01008.(Paper)
Li, Y., Yan, J., Zhou, Y. and Yang, J., 2010, September. Optimum subspace learning and error correction for tensors. In European Conference on Computer Vision (pp. 790-803). Springer, Berlin, Heidelberg.(Paper)
An extension of matrix RPCA to tensor recovery- A summary Tensor is modeled as a combination of a low-rank component and a sparse component
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Yang, Y., Feng, Y., & Suykens, J. A. (2015). Robust low-rank tensor recovery with regularized redescending M-estimator. IEEE transactions on neural networks and learning systems, 27(9), 1933-1946.
Zhao, Qibin, et al. "Tensor ring decomposition." arXiv preprint arXiv:1606.05535 (2016).(Paper)(Matlab Code)
Oseledets, Ivan V. "Tensor-train decomposition." SIAM Journal on Scientific Computing 33.5 (2011): 2295-2317. (Paper) (Matlab code) (Tensorflow code)