Scaled Nuclear Norm Minimization for Low-Rank Tensor Completion
This provides an incremental improvement for tensor completion in machine learning and data analysis applications.
The paper tackles the problem of recovering low-TT-rank tensors from incomplete samples by proposing a weighted sum of nuclear norms minimization approach, showing it requires significantly fewer samples than existing sum-of-nuclear-norms methods.
Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in recovering a low-Tucker-rank sampled tensor. In this paper, we propose to recover a low-TT-rank sampled tensor by minimizing a weighted sum of nuclear norms of unfoldings of the tensor. We provide numerical results to show that our proposed method requires significantly less number of samples to recover to the original tensor in comparison with simply minimizing the sum of nuclear norms since the structure of the unfoldings in the TT tensor model is fundamentally different from that of matricizations in the Tucker tensor model.