A Comparative Analysis of Matrix Factorization Models for Collaborative Filtering: From Basic SVD to SVD++

Recommendation systems have permeated society and everyone’s daily life with the expanding use of applications. It plays an important role in providing recommendations to active users based on either their historical interests or interests shown by similar users. This paper aims to introduce several components of a recommendation system, such as Collaborative Filtering (CF) and Matrix Factorization, and combining the dominant approach and main technique: Singular Value Decomposition (SVD). Additionally, with the advances in technology, various recently established SVD-based models are mentioned in this paper, attempting to give an answer to the question that though studies have shown the coexistence of advantages and disadvantages for each mode, the trade-offs between their predictive accuracy, computational cost, and robustness to data sparsity have still not been fully answered. Furthermore, this paper concentrates on the comparison and analysis of diverse matrix factorization variants, meanwhile evaluating their performances. For instance, basic SVD, BiasSVD, and SVD++. Finding indicates that SVD shows more efficiency in small-scale datasets, BiasSVD is suitable for cases with noticeable biases, and SVD++ gives high-quality results when handling both explicit and implicit feedback data. This study provides practical guidelines for practitioners to select the most desirable model based on their existing database.