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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 35 / No. 12: AAAI-21 Technical Tracks 12

Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion

February 1, 2023

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Authors

Yu-Bang Zheng

School of Mathematical Sciences, University of Electronic Science and Technology of China


Ting-Zhu Huang

School of Mathematical Sciences, University of Electronic Science and Technology of China


Xi-Le Zhao

School of Mathematical Sciences, University of Electronic Science and Technology of China


Qibin Zhao

Tensor Learning Team, RIKEN Center for Advanced Intelligence Project (AIP) School of Automation, Guangdong University of Technology


Tai-Xiang Jiang

School of Economic Information Engineering, Southwestern University of Finance and Economics


DOI:

10.1609/aaai.v35i12.17321


Abstract:

The popular tensor train (TT) and tensor ring (TR) decompositions have achieved promising results in science and engineering. However, TT and TR decompositions only establish an operation between adjacent two factors and are highly sensitive to the permutation of tensor modes, leading to an inadequate and inflexible representation. In this paper, we propose a generalized tensor decomposition, which decomposes an Nth-order tensor into a set of Nth-order factors and establishes an operation between any two factors. Since it can be graphically interpreted as a fully-connected network, we named it fully-connected tensor network (FCTN) decomposition. The superiorities of the FCTN decomposition lie in the outstanding capability for characterizing adequately the intrinsic correlations between any two modes of tensors and the essential invariance for transposition. Furthermore, we employ the FCTN decomposition to one representative task, i.e., tensor completion, and develop an efficient solving algorithm based on proximal alternating minimization. Theoretically, we prove the convergence of the developed algorithm, i.e., the sequence obtained by it globally converges to a critical point. Experimental results substantiate that the proposed method compares favorably to the state-of-the-art methods based on other tensor decompositions.

Topics: AAAI

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HOW TO CITE:

Yu-Bang Zheng||Ting-Zhu Huang||Xi-Le Zhao||Qibin Zhao||Tai-Xiang Jiang Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion Proceedings of the AAAI Conference on Artificial Intelligence (2021) 11071-11078.

Yu-Bang Zheng||Ting-Zhu Huang||Xi-Le Zhao||Qibin Zhao||Tai-Xiang Jiang Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion AAAI 2021, 11071-11078.

Yu-Bang Zheng||Ting-Zhu Huang||Xi-Le Zhao||Qibin Zhao||Tai-Xiang Jiang (2021). Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion. Proceedings of the AAAI Conference on Artificial Intelligence, 11071-11078.

Yu-Bang Zheng||Ting-Zhu Huang||Xi-Le Zhao||Qibin Zhao||Tai-Xiang Jiang. Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion. Proceedings of the AAAI Conference on Artificial Intelligence 2021 p.11071-11078.

Yu-Bang Zheng||Ting-Zhu Huang||Xi-Le Zhao||Qibin Zhao||Tai-Xiang Jiang. 2021. Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion. "Proceedings of the AAAI Conference on Artificial Intelligence". 11071-11078.

Yu-Bang Zheng||Ting-Zhu Huang||Xi-Le Zhao||Qibin Zhao||Tai-Xiang Jiang. (2021) "Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion", Proceedings of the AAAI Conference on Artificial Intelligence, p.11071-11078

Yu-Bang Zheng||Ting-Zhu Huang||Xi-Le Zhao||Qibin Zhao||Tai-Xiang Jiang, "Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion", AAAI, p.11071-11078, 2021.

Yu-Bang Zheng||Ting-Zhu Huang||Xi-Le Zhao||Qibin Zhao||Tai-Xiang Jiang. "Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion". Proceedings of the AAAI Conference on Artificial Intelligence, 2021, p.11071-11078.

Yu-Bang Zheng||Ting-Zhu Huang||Xi-Le Zhao||Qibin Zhao||Tai-Xiang Jiang. "Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion". Proceedings of the AAAI Conference on Artificial Intelligence, (2021): 11071-11078.

Yu-Bang Zheng||Ting-Zhu Huang||Xi-Le Zhao||Qibin Zhao||Tai-Xiang Jiang. Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion. AAAI[Internet]. 2021[cited 2023]; 11071-11078.


ISSN: 2374-3468


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