# Targeted matrix completion

## TL;DR

This paper introduces Targeted, a framework for completing matrices containing low-rank submatrices, achieving lower reconstruction errors by separately processing these submatrices with state-of-the-art methods.

## Contribution

The paper presents a novel framework that identifies low-rank submatrices within larger matrices and applies targeted completion, improving accuracy over classical methods.

## Key findings

- Targeted reduces reconstruction errors significantly.
- It effectively identifies low-rank submatrices from partial observations.
- Achieves better performance than classical matrix completion methods.

## Abstract

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume that the input partially-observed matrix is low rank. The success of these methods depends on the number of observed entries and the rank of the matrix; the larger the rank, the more entries need to be observed in order to accurately complete the matrix. In this paper, we deal with matrices that are not necessarily low rank themselves, but rather they contain low-rank submatrices. We propose Targeted, which is a general framework for completing such matrices. In this framework, we first extract the low-rank submatrices and then apply a matrix-completion algorithm to these low-rank submatrices as well as the remainder matrix separately. Although for the completion itself we use state-of-the-art completion methods, our results demonstrate that Targeted achieves significantly smaller reconstruction errors than other classical matrix-completion methods. One of the key technical contributions of the paper lies in the identification of the low-rank submatrices from the input partially-observed matrices.