Efficient Low Rank Tensor Ring Completion
This work addresses data completion challenges in computer vision by introducing a more efficient tensor-based method, though it is incremental as it builds on prior tensor decomposition techniques.
The paper tackles the problem of tensor completion by proposing an algorithm using tensor ring decompositions with matrix product state representation and spectral initialization, showing that it outperforms existing tensor train methods in real computer vision settings, with numerical comparisons demonstrating improved expressive power.
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and analyze the computational complexity of the proposed algorithm. We numerically compare it with existing methods that employ a low rank tensor train approximation for data completion and show that our method outperforms the existing ones for a variety of real computer vision settings, and thus demonstrate the improved expressive power of tensor ring as compared to tensor train.