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Randomized singular value decomposition (rsvd) is a fast probabilistic algorithm that canbe used to compute the near optimal low-rank singular value decomposition of massive data sets with high accuracy.The key idea is to compute a compressed representationof the data to capture the essential information. This compressed representation can then be used to obtainthe low-rank singular value decomposition decomposition. The rsvd package provides one of the fastest routines for low-rank matrix approximations in R, as far as we know.
The computational advantage becomes pronounced with an increasing matrix dimension (here target-rank k=50):

The singular value decomposition plays a central role in data analysis and scientific computing.The SVD is also widely used for computing(randomized) principal component analysis (PCA), a linear dimensionality reduction technique.Randomized PCA (rpca) uses the approximated singular value decompositionto compute the most significant principal components. This package also includes afunction to compute (randomized) robust principal component analysis (RPCA).In addition several plot functions are provided. See for further details:�Randomized Matrix Decompositions using R�.

library(rsvd)data(tiger)# Image compression using randomized SVDs<- rsvd(tiger,k=150)tiger.re=s$u%*% diag(s$d)%*% t(s$v)# reconstruct image# Display orginal and reconstrucuted imagepar(mfrow=c(1,2))image(tiger,col= gray((0:255)/255))image(tiger.re,col= gray((0:255)/255))

Here are the results:

and the speedup gained over the base SVD function:

library(microbenchmark)timing_svd<- microbenchmark('SVD'= svd(tiger,nu=150,nv=150),'rSVD'= rsvd(tiger,k=150),times=50)print(timing_svd,unit='s')

Install the rsvd package via CRAN

install.packages("rsvd")

You can also install the development version from GitHub usingdevtools:

devtools::install_github("erichson/rsvd")

The source packge can be obtained here:CRAN: rsvd.

• Several small issues are fixed.
• Thanks to Aaron Lun, who has fixed a bug in the rsvd function that occured when nu=0 or nv=0.

• Support for non-default matrix types to deal with large-scale matrices that are held on file, added by Aaron Lun.
• Fixed a bug which occured runninig rpca with k=1 and retx=TRUE, discovered by Will.

• Erichson NB, Voronin S, Brunton SL, Kutz JN (2019). Randomized Matrix Decompositions Using R. Journal of Statistical Software, 89(11), 1–48. doi: 10.18637/jss.v089.i11.
• Sergey Voronin, Per-Gunnar Martinsson. RSVDPACK: Subroutines for computing partial singular value decompositions via randomized sampling on single core, multi core, and GPU architectures. (2015)
• Nathan Halko, et al. Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. (2011)

@Article{,    title = {Randomized Matrix Decompositions Using {R}},    author = {N. Benjamin Erichson and Sergey Voronin and Steven L.      Brunton and J. Nathan Kutz},    journal = {Journal of Statistical Software},    year = {2019},    volume = {89},    number = {11},    pages = {1--48},    doi = {10.18637/jss.v089.i11},}