Tensor Wheel Decomposition and Its Tensor Completion Application
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作者:
Wu, Zhong-Cheng
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机构:
Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Peoples R China
Wu, Zhong-Cheng
[1
]
Huang, Ting-Zhu
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机构:
Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Peoples R China
Huang, Ting-Zhu
[1
]
Deng, Liang-Jian
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Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Peoples R China
Deng, Liang-Jian
[1
]
Dou, Hong-Xia
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机构:
Xihua Univ, Sch Sci, Chengdu, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Peoples R China
Dou, Hong-Xia
[2
]
Meng, Deyu
论文数: 0引用数: 0
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机构:
Xi An Jiao Tong Univ, Sch Math & Stat, Xian, Peoples R China
Pazhou Lab Huangpu, Huangpu, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Peoples R China
Meng, Deyu
[3
,4
]
机构:
[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Peoples R China
[2] Xihua Univ, Sch Sci, Chengdu, Peoples R China
[3] Xi An Jiao Tong Univ, Sch Math & Stat, Xian, Peoples R China
[4] Pazhou Lab Huangpu, Huangpu, Peoples R China
来源:
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 35 (NEURIPS 2022)
|
2022年
Recently, tensor network (TN) decompositions have gained prominence in computer vision and contributed promising results to high-order data recovery tasks. However, current TN models are rather being developed towards more intricate structures to pursue incremental improvements, which instead leads to a dramatic increase in rank numbers, thus encountering laborious hyper-parameter selection, especially for higher-order cases. In this paper, we propose a novel TN decomposition, dubbed tensor wheel (TW) decomposition, in which a high-order tensor is represented by a set of latent factors mapped into a specific wheel topology. Such decomposition is constructed starting from analyzing the graph structure, aiming to more accurately characterize the complex interactions inside objectives while maintaining a lower hyper-parameter scale, theoretically alleviating the above deficiencies. Furthermore, to investigate the potentiality of TW decomposition, we provide its one numerical application, i.e., tensor completion (TC), yet develop an efficient proximal alternating minimization-based solving algorithm with guaranteed convergence. Experimental results elaborate that the proposed method is significantly superior to other tensor decomposition-based state-of-the-art methods on synthetic and real-world data, implying the merits of TW decomposition. The code is available at: https://github.com/zhongchengwu/code_TWDec.
机构:
Univ Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R China
Chen, Yong
;
Huang, Ting-Zhu
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Univ Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R China
Huang, Ting-Zhu
;
He, Wei
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机构:
RIKEN, Geoinformat Unit, RIKEN Ctr Adv Intelligence Project, Tokyo 1030027, JapanUniv Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R China
He, Wei
;
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Yokoya, Naoto
;
Zhao, Xi-Le
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Univ Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R China
机构:
Tokyo Inst Technol, Dept Commun & Integrated Syst, Meguro Ku, Tokyo 1528550, JapanTokyo Inst Technol, Dept Commun & Integrated Syst, Meguro Ku, Tokyo 1528550, Japan
Gandy, Silvia
;
Recht, Benjamin
论文数: 0引用数: 0
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机构:
Univ Wisconsin, Dept Comp Sci, Madison, WI 53706 USATokyo Inst Technol, Dept Commun & Integrated Syst, Meguro Ku, Tokyo 1528550, Japan
机构:
Univ Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R China
Chen, Yong
;
Huang, Ting-Zhu
论文数: 0引用数: 0
h-index: 0
机构:
Univ Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R China
Huang, Ting-Zhu
;
He, Wei
论文数: 0引用数: 0
h-index: 0
机构:
RIKEN, Geoinformat Unit, RIKEN Ctr Adv Intelligence Project, Tokyo 1030027, JapanUniv Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R China
He, Wei
;
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h-index:
机构:
Yokoya, Naoto
;
Zhao, Xi-Le
论文数: 0引用数: 0
h-index: 0
机构:
Univ Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Res Ctr Image & Vis Comp, Chengdu 611731, Peoples R China
机构:
Tokyo Inst Technol, Dept Commun & Integrated Syst, Meguro Ku, Tokyo 1528550, JapanTokyo Inst Technol, Dept Commun & Integrated Syst, Meguro Ku, Tokyo 1528550, Japan
Gandy, Silvia
;
Recht, Benjamin
论文数: 0引用数: 0
h-index: 0
机构:
Univ Wisconsin, Dept Comp Sci, Madison, WI 53706 USATokyo Inst Technol, Dept Commun & Integrated Syst, Meguro Ku, Tokyo 1528550, Japan