Randomized Matrix Decompositions using R

By N. Benjamin Erichson, Sergey Voronin, Steven L. Brunton, J. Nathan Kutz. 2016

154 citations recorded by the source corpus.

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 \proglang{R} 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.

Subfields: Artificial Intelligence, Computational Mathematics, Computational Mechanics

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In Artificial Intelligence

1. Andrews Cordolino Sobral
2. Thierry Bouwmans
3. Soon Ki Jung
4. El-Hadi Zahzah
5. Sajid Javed

In Computational Mechanics

1. Thierry Bouwmans
2. Soon Ki Jung
3. El-Hadi Zahzah
4. Andrews Cordolino Sobral
5. Sajid Javed

Citations in the corpus

• Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, methodology): “ck-SVD Chai et al. (2013) [52] Limited Memory SVD (LMSVD) Liu et al. (2013) [237] Symmetric Low-Rank Product-Gauss-Newton (SLRPGN) Liu et al. (2014) [238] randomized SVD (rSVD) Erichson et al. (2016) [98] Table 17 Principal Component Pursuit: A Complete Overview (Part 3). The first column indicates t”
• Overview and comparative study of dimensionality reduction techniques for high dimensional data (2020, unknown): “SVD follows a de-facto standard for DR process in generic data sets and provides an optimal level of DR for linear projections [71,72] .”