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
You can also install the development version from GitHub using devtools:
The source packge can be obtained here: CRAN: rsvd.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.