# Matrix Completion in the Unit Hypercube via Structured Matrix Factorization

## TL;DR

This paper introduces two novel matrix factorization models, EMF and SMF, designed for constrained matrix completion tasks within the unit hypercube, specifically applied to predicting VFX artists' efficiency.

## Contribution

The paper presents two new matrix factorization models tailored for bounded matrix completion, incorporating interpretability and probabilistic modeling for efficiency prediction.

## Key findings

- Models outperform baseline methods on VFX dataset
- Effective in predicting efficiencies within [0, 1] bounds
- Validated on multiple datasets with bounded values

## Abstract

Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual effects (VFX) in film shots. We tackle this challenge by using a two-fold approach: first, we transform this task into a constrained matrix completion problem with entries bounded in the unit interval [0, 1]; second, we propose two novel matrix factorization models that leverage our knowledge of the VFX environment. Our first approach, expertise matrix factorization (EMF), is an interpretable method that structures the latent factors as weighted user-item interplay. The second one, survival matrix factorization (SMF), is instead a probabilistic model for the underlying process defining employees' efficiencies. We show the effectiveness of our proposed models by extensive numerical tests on our VFX dataset and two additional datasets with values that are also bounded in the [0, 1] interval.