High-order tensor completion via gradient-based optimization under tensor train format
作者：
Highlights：
• By employing tensor-train (TT) decomposition, we propose a gradientbased tensor completion algorithm named TT-WOPT which is of low computational complexity and shows high computational efficiency.
• Based on stochastic gradient descent method, we propose the TT-SGD algorithm which possesses extremely low computational complexity in every iteration and can be applied to solving large-scale tensor completion problems.
• We propose a higher-order tensorization method named VDT which transforms visual data into higher-order tensors. By applying the VDT method, the performance of TT-WOPT and TT-SGD are improved.
摘要
•By employing tensor-train (TT) decomposition, we propose a gradientbased tensor completion algorithm named TT-WOPT which is of low computational complexity and shows high computational efficiency.•Based on stochastic gradient descent method, we propose the TT-SGD algorithm which possesses extremely low computational complexity in every iteration and can be applied to solving large-scale tensor completion problems.•We propose a higher-order tensorization method named VDT which transforms visual data into higher-order tensors. By applying the VDT method, the performance of TT-WOPT and TT-SGD are improved.
论文关键词：Tensor completion,Visual data recovery,Tensor train decomposition,Higher-order tensorization,Gradient-based optimization
论文评审过程：Received 9 April 2018, Revised 30 November 2018, Accepted 30 November 2018, Available online 6 December 2018, Version of Record 12 March 2019.
论文官网地址：https://doi.org/10.1016/j.image.2018.11.012
