# Matrix Completion With Selective Sampling

## TL;DR

This paper explores matrix completion by designing selective sampling strategies based on known matrix structures, aiming to improve reconstruction efficiency over traditional uniform sampling methods.

## Contribution

It introduces methods for selective sampling in matrix completion when partial structural knowledge of the matrix is available, moving beyond uniform sampling assumptions.

## Key findings

- Selective sampling improves reconstruction accuracy
- Structural knowledge guides better sampling strategies
- Proposed methods outperform uniform sampling in experiments

## Abstract

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization problem. Almost all previous work assumes no explicit structure of the matrix and uses uniform sampling to decide the observed entries. We suggest methods for selective sampling in the case where we have some knowledge about the structure of the matrix and are allowed to design the observation set.