Matrix Completion and Tensor Rank

TL;DR

This paper demonstrates that low rank matrix completion can be transformed into a tensor rank determination problem, providing a new perspective on solving matrix completion tasks.

Contribution

It introduces a reduction from matrix completion to tensor rank computation, offering a novel approach to address low rank matrix problems.

Findings

Reduction from matrix completion to tensor rank problem

Potential new algorithms for matrix completion based on tensor methods

Theoretical insights into the relationship between matrices and tensors

Abstract

In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.