Tensor Wheel Decomposition and Its Tensor Completion Application

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.

Authors

• Zhong-Cheng Wu
• Ting-Zhu Huang
• Liang-Jian Deng University of Electronic Science and Technology of China
• Hong-Xia Dou
• Deyu Meng Xi'an Jiaotong University Pengcheng Laboratory Macau University of Science and Technology

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