Two heuristics solving low tensor train rank tensor completion

In this paper we consider the low rank tensor completion problem based on the tensor train (TT) rank. We propose two models for this problem. The one is based on the nuclear norm heuristic, and the other is based on the factorization heuristic. We apply the ADMM and the Douglas-Rachford splitting technique to the nuclear norm model. And for the factorization model, we utilize the alternating linear scheme (ALS) and the modified alternating linear scheme (MALS), which are special block coordinate descent methods for minimization tasks in the TT format, to reduce the computation cost of the subproblems. We then apply our algorithms to various synthetic and real datasets. The results are compared with some other popular tensor completion methods, which demonstrate that our algorithms are competitive to these methods.