# Randomized Matrix Decompositions using R

arXiv: https://arxiv.org/abs/1608.02148 · HTML: https://mlsanity.com/paper/1608.02148/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2016.

## Built on by (most cited first, 13 of 13)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations](https://mlsanity.com/paper/2104.14034/) (2021)
- [Orthogonal Features Based EEG Signals Denoising Using Fractional and Compressed One-Dimensional CNN AutoEncoder](https://mlsanity.com/paper/2104.08120/) (2021)
- [rSVDdpd: A Robust Scalable Video Surveillance Background Modelling Algorithm](https://mlsanity.com/paper/2109.10680/) (2021)
- [Coupled and Uncoupled Dynamic Mode Decomposition in Multi-Compartmental Systems with Applications to Epidemiological and Additive Manufacturing Problems](https://mlsanity.com/paper/2110.06375/) (2021)
- [Quantifying Epistemic Uncertainty in Diffusion Models](https://mlsanity.com/paper/2602.09170/) (2026)
- [A Highly Effective Low-Rank Compression of Deep Neural Networks with Modified Beam-Search and Modified Stable Rank](https://mlsanity.com/paper/2111.15179/) (2021)
- [Enhancing Dynamic Mode Decomposition Workflow with In-Situ Visualization and Data Compression](https://mlsanity.com/paper/2208.07767/) (2022)
- [Orthogonal Features-based EEG Signal Denoising using Fractionally Compressed AutoEncoder](https://mlsanity.com/paper/2102.08083/) (2021)
- [A Coupled Random Projection Approach to Large-Scale Canonical Polyadic Decomposition](https://mlsanity.com/paper/2105.04084/) (2021)
- [Improved analysis of randomized SVD for top-eigenvector approximation](https://mlsanity.com/paper/2202.07992/) (2022)
- [Optimized Dynamic Mode Decomposition for Reconstruction and Forecasting of Atmospheric Chemistry Data](https://mlsanity.com/paper/2404.12396/) (2024)

## Abstract (arXiv)

Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality reduction, and data compression. Massive datasets, however, pose a computational challenge for traditional algorithms, placing significant constraints on both memory and processing power. Recently, the powerful concept of randomness has been introduced as a strategy to ease the computational load. The essential idea of probabilistic algorithms is to employ some amount of randomness in order to derive a smaller matrix from a high-dimensional data matrix. The smaller matrix is then used to compute the desired low-rank approximation. Such algorithms are shown to be computationally efficient for approximating matrices with low-rank structure. We present the proglangR package rsvd, and provide a tutorial introduction to randomized matrix decompositions. Specifically, randomized routines for the singular value decomposition, (robust) principal component analysis, interpolative decomposition, and CUR decomposition are discussed. Several examples demonstrate the routines, and show the computational advantage over other methods implemented in R.