Tensor Theory

Transform-based Tensor Model

(The low-tubal-rank tensor model is a special case when the transform is discrete Fourier transform.)

* [NIPS Workshop] W. Lu, X.-Y. Liu, Q. Wu, Y. Sun, A. Walid. Transform-based multilinear dynamical system for tensor time series analysis. NIPS Workshop on Modeling and Decision-Making in the Spatiotemporal Domain, 2018.

* X.-Y. Liu and X. Wang. Fourth-order tensor space with two-dimensional discrete transforms. arXiv,2017.

* [TIT] X.-Y. Liu, S. Aeron, V. Aggarwal, X. Wang. Low-tubal-rank tensor completion using alternating minimization. (Major Revision) IEEE Transactions on Information Theory.

* [AAAI] F. Jiang, X.-Y. Liu, H. Lu, R. Shen. Efficient multi-dimensional tensor sparse coding using t-linear combinations. AAAI, 2018.

* [ICME] T. Deng, F. Qian,  X.-Y. Liu, M. Zhang, A. Walid. Tensor sensing for RF tomographic imaging. IEEE ICME, 2018.

* [ICASSP] C. Li, Y. Sun, X.-Y. Liu, Y. Li. Tensor subspace detection with tubal-sampling and elementwise-sampling. IEEE ICASSP, 2018.

* [ICASSPF. Jiang, X.-Y. Liu, H. Lu, R. Shen. Anisotropic total variation regularized low-rank tensor completion based on tensor nuclear norm for color image inpainting. IEEE ICASSP, 2018.

* C. Zhu, L. Xu, X.-Y. Liu, F. Qian. Tensor-generative adversarial network with two-dimensional sparse coding: application to real-time indoor localization. IEEE International Conference on Communications (ICC), 2018.

* [ICME] F. Jiang, X.-Y. Liu, H. Lu, R. Shen. Graph regularized tensor sparse coding for image representation. IEEE ICME, 2017.

* [TMC] X.-Y. Liu, S. Aeron, V. Aggarwal, X. Wang, M.-Y. Wu. Adaptive sampling of RF fingerprints for fine-grained indoor localization. IEEE Transactions on Mobile Computing, 2016.

* [ICASSP] X.-Y. Liu, S. Aeron, V. Aggarwal, X. Wang, M.-Y. Wu. Tensor completion via adaptive sampling of tensor fibers: application to efficient indoor RF fingerprinting. IEEE ICASSP, 2016.

 

*[JMLR] M. Ashraphijuo, X. Wang. Fundamental conditions for low-CP-rank tensor completion. The Journal of Machine Learning Research18(1), pp.2116-2145, 2017.

*[JMLR] M. Ashraphijuo, X. Wang, V. Aggarwal. Rank determination for low-rank data completion. The Journal of Machine Learning Research18(1), pp.3422-3450, 2017

Tensor Operations

Tensor Product
Multilinear Algebra

Tensor Models

Tensor SVD Decompositions
Low CP-rank
Low Tucker-rank
Tensor-Train (Tensor-Ring)
Hierarchical Tensor Decomposition

Applications

Big Data Analysis
Deep Learning

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