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Tensor train (TT) decomposition has drawn people's attention due to itspowerful representation ability and performance stability in high-ordertensors. In this paper, we propose a novel approach to recover the missingentries of incomplete data represented by higher-order tensors. We attempt tofind the low-rank TT decomposition of the incomplete data which captures thelatent features of the whole data and then reconstruct the missing entries. Byapplying gradient descent algorithms, tensor completion problem is efficientlysolved by optimization models. We propose two TT-based algorithms: Tensor TrainWeighted Optimization (TT-WOPT) and Tensor Train Stochastic Gradient Descent(TT-SGD) to optimize TT decomposition factors. In addition, a method namedVisual Data Tensorization (VDT) is proposed to transform visual data intohigher-order tensors, resulting in the performance improvement of ouralgorithms. The experiments in synthetic data and visual data show highefficiency and performance of our algorithms compared to the state-of-the-artcompletion algorithms, especially in high-order, high missing rate, andlarge-scale tensor completion situations.

High-dimension Tensor Completion via Gradient-based Optimization Under Tensor-train Format