# An Introduction to Matrix factorization and Factorization Machines in Recommendation System, and Beyond

arXiv: https://arxiv.org/abs/2203.11026 · HTML: https://mlsanity.com/paper/2203.11026/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 9 references that are in the map.
- First posted on arXiv 12 Mar 2022.

## Builds on (most cited first, 2 of 2)

- [Deep & Cross Network for Ad Click Predictions](https://mlsanity.com/paper/1708.05123/) (2017)
- [Field-aware Factorization Machines in a Real-world Online Advertising System](https://mlsanity.com/paper/1701.04099/) (2017)

## Built on by (most cited first, 5 of 5)

- [Embedding in Recommender Systems: A Survey](https://mlsanity.com/paper/2310.18608/) (2023)
- [Doing More with Less: A Survey on Routing Strategies for Resource Optimisation in Large Language Model-Based Systems](https://mlsanity.com/paper/2502.00409/) (2025)
- [Conv4Rec: A 1-by-1 Convolutional AutoEncoder for User Profiling through Joint Analysis of Implicit and Explicit Feedbacks](https://mlsanity.com/paper/2509.07499/) (2025)
- [Efficient Graph based Recommender System with Weighted Averaging of Messages](https://mlsanity.com/paper/2209.15238/) (2022)
- [Revisiting Positive Samples in Graph Contrastive Learning: From the Perspective of Message Passing](https://mlsanity.com/paper/2606.10284/) (2026)

## Abstract (arXiv)

This paper aims at a better understanding of matrix factorization (MF), factorization machines (FM), and their combination with deep algorithms' application in recommendation systems. Specifically, this paper will focus on Singular Value Decomposition (SVD) and its derivations, e.g Funk-SVD, SVD++, etc. Step-by-step formula calculation and explainable pictures are displayed. What's more, we explain the DeepFM model in which FM is assisted by deep learning. Through numerical examples, we attempt to tie the theory to real-world problems.