Decomposition Approach for Low-rank Matrix Completion

TL;DR

This paper introduces a novel low-rank matrix completion method using matrix decomposition, which reduces computational complexity and can be integrated with existing methods, applicable across various fields beyond real numbers.

Contribution

The paper presents a divide-and-conquer decomposition approach that avoids norm minimization and SVD, enabling broader application and improved efficiency in matrix completion.

Findings

Reduces computation and storage requirements.

Can be integrated with existing matrix completion methods.

Applicable to arbitrary fields including finite fields.

Abstract

In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank completed matrix. The divide-and-conquer approach can significantly reduce computation complexity and storage requirement. Moreover, the proposed decomposition method can be naturally incorporated into any existing matrix completion methods to attain further gain. Unlike most existing approaches, the proposed method is not based on norm minimization nor SVD decomposition. This makes it possible to be applied beyond real domain and can be used in arbitrary fields including finite fields.