Tensor Completion by Alternating Minimization under the Tensor Train (TT) Model

TL;DR

This paper introduces a tensor completion algorithm based on alternating minimization within the tensor train (TT) model, leveraging MPS representation, and demonstrates its superior performance over existing methods through numerical comparisons.

Contribution

It proposes a novel tensor completion algorithm using alternating minimization on MPS representation within the TT model, improving over existing low-rank tensor train methods.

Findings

The proposed method outperforms existing tensor completion algorithms in various real data scenarios.

The algorithm's computational complexity is analyzed and discussed.

Numerical experiments show superior accuracy and efficiency compared to recent methods.

Abstract

Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated in part by the success of matrix completion algorithms which alternate over the (low-rank) factors. We comment on the computational complexity of the proposed algorithm and numerically compare it with existing methods employing low rank tensor train approximation for data completion as well as several other recently proposed methods. We show that our method is superior to existing ones for a variety of real settings.