Randomized Matrix Decompositions using R

The singular value decomposition (SVD) is among the most ubiquitous matrix factorizations. Specifically, it is a cornerstone algorithm for data analysis, dimensionality reduction and data compression. However, despite modern computer power, massive datasets pose a computational challenge for traditional SVD algorithms. We present the R package rsvd, which enables the fast computation of the SVD and related methods, facilitated by randomized algorithms. The rsvd package provides routines for computing the randomized singular value decomposition, randomized principal component analysis and randomized robust principal component analysis. Randomized algorithms provide an efficient computational framework for reducing the computational demands of traditional (deterministic) matrix factorizations. The key idea is to compute a compressed representation of the data using random sampling. This smaller (compressed) matrix captures the essential information that can then be used to obtain a low-rank matrix approximation. Several numerical examples demonstrate the usage of the rsvd package. The results show substantial accelerated computational times using the powerful concept of randomization.