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

By Yuefeng Zhang et al

Published on March 12, 2022

Read the original document by opening this link in a new tab.

Table of Contents

1 Introduction and Overview
1.1 Problem Definition
1.2 Matrix Factorization (MF)
1.2.1 MF for Different Data Sets
1.2.2 Comparison between MF and Collaborative Filtering Algorithms
2 Matrix Factorization (MF)
2.1 Traditional SVD
2.1.1 Example - Complete Matrix
2.1.2 Example - Incomplete Matrix
2.1.3 Example - Numerical Decomposition of Matrices
2.2 Funk-SVD
2.3 SVD++
3 Factorization Machine (FM)
3.0.1 Field-Aware Factorization Machine (FFM)
3.1 With Deep Learning
3.1.1 DeepFM
3.1.2 Model Ensemble
3.1.3 Optimization Algorithms

Summary

This paper provides an in-depth exploration of matrix factorization (MF), factorization machines (FM), and their integration with deep learning algorithms for recommendation systems. It delves into Singular Value Decomposition (SVD) and its variations like Funk-SVD, SVD++, explaining step-by-step formula calculations and providing illustrative diagrams. It also discusses the DeepFM model, combining FM with deep learning, and demonstrates the application through numerical examples. The paper compares MF with collaborative filtering algorithms, emphasizing the role of MF in auto-completing score matrices and its efficiency in memory and time complexity. Traditional SVD is explained in detail, showcasing its use in decomposing matrices and its significance in real-world recommendation scenarios. The authors present examples of complete and incomplete matrices, illustrating the power of SVD in dimensionality reduction and matrix completion. Overall, the paper offers insights into the theoretical foundations and practical applications of matrix factorization and factorization machines in recommendation systems.