# Adaptive Matrix Completion for the Users and the Items in Tail

## TL;DR

This paper addresses the challenge of skewed rating distributions in recommender systems by developing adaptive matrix completion methods that improve predictions for users and items with few ratings.

## Contribution

The authors introduce four novel matrix completion approaches that adapt to rating frequency, enhancing prediction accuracy for sparse data in recommender systems.

## Key findings

- Proposed methods outperform traditional approaches on sparse data.
- Adaptive techniques improve accuracy for users and items with few ratings.
- Skewed rating distribution impacts matrix completion effectiveness.

## Abstract

Recommender systems are widely used to recommend the most appealing items to users. These recommendations can be generated by applying collaborative filtering methods. The low-rank matrix completion method is the state-of-the-art collaborative filtering method. In this work, we show that the skewed distribution of ratings in the user-item rating matrix of real-world datasets affects the accuracy of matrix-completion-based approaches. Also, we show that the number of ratings that an item or a user has positively correlates with the ability of low-rank matrix-completion-based approaches to predict the ratings for the item or the user accurately. Furthermore, we use these insights to develop four matrix completion-based approaches, i.e., Frequency Adaptive Rating Prediction (FARP), Truncated Matrix Factorization (TMF), Truncated Matrix Factorization with Dropout (TMF + Dropout) and Inverse Frequency Weighted Matrix Factorization (IFWMF), that outperforms traditional matrix-completion-based approaches for the users and the items with few ratings in the user-item rating matrix.