Tensor Missing Value Recovery with Tucker Thresholding Method

In this paper, a tensor missing value recovery method on the tensor Tucker decomposition is presented. The contribution of this paper is to extend matrix shrinkage operator to the tensor Tucker higher-order singular value decomposition operator to obtain the best low-n-rank automatic. To obtain the optimal approximation tensor which is the key factor in recovery missing value of tensors, a tensor Tucker higher-order orthogonal iteration decomposition is presented which can solve the tensor trace norm objective function directly. In order to avoid relaxing the tensor trace norm function, the augment Lagrange multiplier method is adapted to the solving process. Without turning it into the average of the trace norms of all matrices unfolded along each mode, our method has more recovery accuracy and robust than the off-the-shelf method.