Tensor factorization for low-rank tensor completion

• Main Authors: ZHOU, Pan, LU, Canyi, LIN, Zhouchen, ZHANG, Chao
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2017
• Subjects: Tensor Factorization; Tensor Completion; Lowrank Factorization; Databases and Information Systems
• Online Access: https://ink.library.smu.edu.sg/sis_research/9057; https://ink.library.smu.edu.sg/context/sis_research/article/10060/viewcontent/2017_TIP_TCTF.pdf
• Institution: Singapore Management University

Recently, a tensor nuclear norm (TNN) based method [1] was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the lowrank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker (KKT) point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN [1] and matricization methods [2]–[5].