# On the Effectiveness of Low-rank Approximations for Collaborative Filtering compared to Neural Networks

## TL;DR

This paper compares low-rank matrix factorization and deep neural networks for collaborative filtering, finding that low-rank methods outperform neural networks due to better suitability for the task.

## Contribution

The study clarifies why low-rank approximations are more effective than neural networks in pure collaborative filtering tasks without additional features.

## Key findings

- Low-rank methods outperform neural networks in collaborative filtering.
- Deep neural networks' universal approximation impairs latent vector determination.
- Low-rank approximations are better suited for pure collaborative filtering tasks.

## Abstract

Even in times of deep learning, low-rank approximations by factorizing a matrix into user and item latent factors continue to be a method of choice for collaborative filtering tasks due to their great performance. While deep learning based approaches excel in hybrid recommender tasks where additional features for items, users or even context are available, their flexibility seems to rather impair the performance compared to low-rank approximations for pure collaborative filtering tasks where no additional features are used. Recent works propose hybrid models combining low-rank approximations and traditional deep neural architectures with promising results but fail to explain why neural networks alone are unsuitable for this task. In this work, we revisit the model and intuition behind low-rank approximation to point out its suitability for collaborative filtering tasks. In several experiments we compare the performance and behavior of models based on a deep neural network and low-rank approximation to examine the reasons for the low effectiveness of traditional deep neural networks. We conclude that the universal approximation capabilities of traditional deep neural networks severely impair the determination of suitable latent vectors, leading to a worse performance compared to low-rank approximations.