Randomized singular value decomposition (rsvd) is a fast probabilistic algorithm that can be 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 representation of the data to capture the essential information. This compressed representation can then be used to obtain the 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 decomposition to compute the most significant principal components. This package also includes a function 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 SVD
s <- rsvd(tiger, k=150)
tiger.re = s$u %*% diag(s$d) %*% t(s$v) # reconstruct image
# Display orginal and reconstrucuted image
par(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 using devtools:
devtools::install_github("erichson/rsvd")
The source packge can be obtained here: CRAN: rsvd.
@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},
}
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