# Regularized Singular Value Decomposition and Application to Recommender System

arXiv: https://arxiv.org/abs/1804.05090 · HTML: https://mlsanity.com/paper/1804.05090/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2018.

## Built on by (most cited first, 6 of 6)

- [Is Cosine-Similarity of Embeddings Really About Similarity?](https://mlsanity.com/paper/2403.05440/) (2024)
- [Towards a Better Understanding of Linear Models for Recommendation](https://mlsanity.com/paper/2105.12937/) (2021)
- [Posterior Collapse of a Linear Latent Variable Model](https://mlsanity.com/paper/2205.04009/) (2022)
- [Of Spiky SVDs and Music Recommendation](https://mlsanity.com/paper/2307.01212/) (2023)
- [A Comprehensive Review on Non-Neural Networks Collaborative Filtering Recommendation Systems](https://mlsanity.com/paper/2106.10679/) (2021)
- [On the Regularization Landscape for the Linear Recommendation Models](https://mlsanity.com/paper/2609.11876/) (2026)

## Abstract (arXiv)

Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern recognition, artificial intelligence, computer vision, signal processing, etc. In recent applications, regularization becomes an increasing trend. In this paper, we present a regularized SVD (RSVD), present an efficient computational algorithm, and provide several theoretical analysis. We show that although RSVD is non-convex, it has a closed-form global optimal solution. Finally, we apply RSVD to the application of recommender system and experimental result show that RSVD outperforms SVD significantly.