  Tensor train (TT) decomposition has drawn people's attention due to its
powerful representation ability and performance stability in high-order
tensors. In this paper, we propose a novel approach to recover the missing
entries of incomplete data represented by higher-order tensors. We attempt to
find the low-rank TT decomposition of the incomplete data which captures the
latent features of the whole data and then reconstruct the missing entries. By
applying gradient descent algorithms, tensor completion problem is efficiently
solved by optimization models. We propose two TT-based algorithms: Tensor Train
Weighted Optimization (TT-WOPT) and Tensor Train Stochastic Gradient Descent
(TT-SGD) to optimize TT decomposition factors. In addition, a method named
Visual Data Tensorization (VDT) is proposed to transform visual data into
higher-order tensors, resulting in the performance improvement of our
algorithms. The experiments in synthetic data and visual data show high
efficiency and performance of our algorithms compared to the state-of-the-art
completion algorithms, especially in high-order, high missing rate, and
large-scale tensor completion situations.

Numerical Analysis;Computer Vision and Pattern Recognition;Machine Learning