L1-norm-Tucker-Tensor-Decomposition

In this repo, we implement algorithms for L1-norm Tucker decomposition of tensors:

Specifically, we implement:

• L1-norm Higher-Order Singular-Value Decomposition (L1-HOSVD) [1], [2]
• L1-norm Higher-Order Orthogonal Iterations (L1-HOOI) [1], [3]

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IEEEXplore:

• [1] https://ieeexplore.ieee.org/document/8910610
• [2] https://ieeexplore.ieee.org/document/8646385
• [3] https://ieeexplore.ieee.org/document/9053701

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Citing

If you use our algorihtms, please cite [1]-[3].

@ARTICLE{l1tucker,
  author={D. G. {Chachlakis} and A. {Prater-Bennette} and P. P. {Markopoulos}},
  journal={IEEE Access}, 
  title={L1-Norm Tucker Tensor Decomposition}, 
  year={2019},
  volume={7},
  number={},
  pages={178454-178465},
  doi={10.1109/ACCESS.2019.2955134}}

[1]	D. G. Chachlakis, A. Prater-Bennette and P. P. Markopoulos, "L1-Norm Tucker Tensor Decomposition," in IEEE Access, vol. 7, pp. 178454-178465, 2019, doi: 10.1109/ACCESS.2019.2955134.

@INPROCEEDINGS{l1hosvd,
  author={P. P. {Markopoulos} and D. G. {Chachlakis} and A. {Prater-Bennette}},
  booktitle={2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)}, 
  title={L1-NORM HIGHER-ORDER SINGULAR-VALUE DECOMPOSITION}, 
  year={2018},
  volume={},
  number={},
  pages={1353-1357},
  doi={10.1109/GlobalSIP.2018.8646385}}

[2]	P. P. Markopoulos, D. G. Chachlakis and A. Prater-Bennette, "L1-NORM HIGHER-ORDER SINGULAR-VALUE DECOMPOSITION," 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP), Anaheim, CA, USA, 2018, pp. 1353-1357, doi: 10.1109/GlobalSIP.2018.8646385.

@INPROCEEDINGS{l1hooi,
  author={D. G. {Chachlakis} and A. {Prater-Bennette} and P. P. {Markopoulos}},
  booktitle={ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, 
  title={L1-Norm Higher-Order Orthogonal Iterations for Robust Tensor Analysis}, 
  year={2020},
  volume={},
  number={},
  pages={4826-4830},
  doi={10.1109/ICASSP40776.2020.9053701}}

[3]	D. G. Chachlakis, A. Prater-Bennette and P. P. Markopoulos, "L1-Norm Higher-Order Orthogonal Iterations for Robust Tensor Analysis," ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Barcelona, Spain, 2020, pp. 4826-4830, doi: 10.1109/ICASSP40776.2020.9053701.

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Related works

The following works might be of interest:

• [4] P. P. Markopoulos, D. G. Chachlakis and E. E. Papalexakis, "The Exact Solution to Rank-1 L1-Norm TUCKER2 Decomposition," in IEEE Signal Processing Letters, vol. 25, no. 4, pp. 511-515, April 2018, doi: 10.1109/LSP.2018.2790901.
• [5] D. G. Chachlakis and P. P. Markopoulos, "Novel Algorithms for Exact and Efficient L1-NORM-BASED Tucker2 Decomposition," 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, AB, 2018, pp. 6294-6298, doi: 10.1109/ICASSP.2018.8461839.
• [6] Dimitris G. Chachlakis, Mayur Dhanaraj, Ashley Prater-Bennette, Panos P. Markopoulos, "Options for multimodal classification based on L1-Tucker decomposition," Proc. SPIE 10989, Big Data: Learning, Analytics, and Applications, 109890O (13 May 2019).
• [7] Dimitris G. Chachlakis, Panos P. Markopoulos, "Robust decomposition of 3-way tensors based on L1-norm," Proc. SPIE 10658, Compressive Sensing VII: From Diverse Modalities to Big Data Analytics, 1065807 (14 May 2018).

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