# Robust SVD Made Easy: A fast and reliable algorithm for large-scale data analysis

arXiv: https://arxiv.org/abs/2402.09754 · HTML: https://mlsanity.com/paper/2402.09754/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 62 references that are in the map.
- First posted on arXiv 15 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [Robust Meta-learning for Mixed Linear Regression with Small Batches](https://mlsanity.com/paper/2006.09702/) (2020)
- [Fast Algorithms for Robust PCA via Gradient Descent](https://mlsanity.com/paper/1605.07784/) (2016)
- [Robust Sub-Gaussian Principal Component Analysis and Width-Independent Schatten Packing](https://mlsanity.com/paper/2006.06980/) (2020)
- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [LazySVD: Even Faster SVD Decomposition Yet Without Agonizing Pain](https://mlsanity.com/paper/1607.03463/) (2016)
- [Minimum Covariance Determinant and Extensions](https://mlsanity.com/paper/1709.07045/) (2017)
- [Optimal Algorithms for L1-subspace Signal Processing](https://mlsanity.com/paper/1405.6785/) (2014)
- [Coherence Pursuit: Fast, Simple, and Robust Principal Component Analysis](https://mlsanity.com/paper/1609.04789/) (2016)
- [Nearly-Linear Time and Streaming Algorithms for Outlier-Robust PCA](https://mlsanity.com/paper/2305.02544/) (2023)
- [Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity](https://mlsanity.com/paper/1507.08788/) (2015)
- [Data Integration Via Analysis of Subspaces (DIVAS)](https://mlsanity.com/paper/2212.00703/) (2022)
- [Robust Orthogonal Complement Principal Component Analysis](https://mlsanity.com/paper/1410.1173/) (2014)
- [The Robustness of Estimator Composition](https://mlsanity.com/paper/1609.01226/) (2016)
- [Robust and Resistant Regularized Covariance Matrices](https://mlsanity.com/paper/2307.15774/) (2023)

## Built on by (most cited first, 4 of 4)

- [Towards Reasoning-Preserving Unlearning in Multimodal Large Language Models](https://mlsanity.com/paper/2512.17911/) (2025)
- [S3LoRA: Safe Spectral Sharpness-Guided Pruning in Adaptation of Agent Planner](https://mlsanity.com/paper/2508.15068/) (2025)
- [Subspace Recovery in Winsorized PCA: Insights into Accuracy and Robustness](https://mlsanity.com/paper/2502.16391/) (2025)
- [D-com: Accelerating Iterative Processing to Enable Low-rank Decomposition of Activations](https://mlsanity.com/paper/2510.13147/) (2025)

## Abstract (arXiv)

The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for robustness or fail in the presence of only a few outliers. This study introduces an efficient algorithm, called Spherically Normalized SVD, for robust SVD approximation that is highly insensitive to outliers, computationally scalable, and provides accurate approximations of singular vectors. The proposed algorithm achieves remarkable speed by utilizing only two applications of a standard reduced-rank SVD algorithm to appropriately scaled data, significantly outperforming competing algorithms in computation times. To assess the robustness of the approximated singular vectors and their subspaces against data contamination, we introduce new notions of breakdown points for matrix-valued input, including row-wise, column-wise, and block-wise breakdown points. Theoretical and empirical analyses demonstrate that our algorithm exhibits higher breakdown points compared to standard SVD and its modifications. We empirically validate the effectiveness of our approach in applications such as robust low-rank approximation and robust principal component analysis of high-dimensional microarray datasets. Overall, our study presents a highly efficient and robust solution for SVD approximation that overcomes the limitations of existing algorithms in the presence of outliers.