Tensor Completion via the CP Decomposition

We propose a new algorithm for tensor completion. The tensor completion problem is about finding the unknown tensor from a given a tensor with partially observed data. While most tensor completion methods use the Tucker model, our new approach uses the canonical polyadic decomposition model to reconstruct the unknown tensor. The unknown tensor is reconstructed by finding the optimal factors through linear least squares and the singular vectors through a proximal algorithm of soft thresholding.