This repo initially implements the algorithm so-called window-based Randomized SVD in the PCAone paper. Now the aim of the package is to implement state-of-the-art Randomized SVD algorithms other than the basic rsvd for R community.
Currently there are 2 versions of RSVD implemented in this package ordered by their accuracy in below.
- winSVD: window based randomized singular value decomposition
- dashSVD: dynamic shifts based randomized singular value decomposition
With surports for a number of matrix type including:
matrixin base R for general dense matrices. or other types can be casted e.g.dgeMatrixdgCMatrixin Matrix package, for column major sparse matricesdgRMatrixin Matrix package, for row major sparse matrices
# install.packages("pcaone") # For the CRAN version
remotes::install_github("Zilong-Li/PCAoneR") # For the latest developing versionThis is a basic example which shows you how to use pcaone:
library(pcaone)
mat <- matrix(rnorm(100*5000), 5000, 100)
res <- pcaone(mat, k = 10)
str(res)
#> List of 3
#> $ d: num [1:10] 80.2 80 79.2 78.9 78.6 ...
#> $ u: num [1:5000, 1:10] -0.01358 -0.01307 0.01905 0.00726 -0.01962 ...
#> $ v: num [1:100, 1:10] 0.0516 -0.0284 0.0251 0.0852 -0.0507 ...
#> - attr(*, "class")= chr "pcaone"We define the accuracy as the error of singular values using results of
RSpectra::svds as truth. For all RSVD, let’s restrict the number of
epochs as 8, i.e. how many times the whole matrix is read through if
it can only be hold on disk.
library(RSpectra) ## svds
library(rsvd) ## regular rsvd
library(pcaone)
load(system.file("extdata", "popgen.rda", package="pcaone") )
A <- popgen - rowMeans(popgen) ## center
k <- 40
system.time(s0 <- RSpectra::svds(A, k = k) )
#> user system elapsed
#> 4.781 0.012 4.797
system.time(s1 <- rsvd::rsvd(A, k = k, q = 4)) ## the number of epochs is two times of power iters, 4*2=8
#> user system elapsed
#> 5.958 0.041 6.005
system.time(s3 <- pcaone(A, k = k, method = "winsvd", p = 7)) ## the number of epochs is 1 + p
#> user system elapsed
#> 0.866 0.011 0.877
system.time(s4 <- pcaone(A, k = k, method = "dashsvd", p = 6))## the number of epochs is 2 + p
#> user system elapsed
#> 0.668 0.025 0.694
par(mar = c(5, 5, 2, 1))
plot(s0$d-s1$d, ylim = c(0, 10), xlab = "PC index", ylab = "Error of singular values", cex = 1.5, cex.lab = 2)
points(s0$d-s3$d, col = "red", cex = 1.5)
points(s0$d-s4$d, col = "blue", cex = 1.5)
legend("top", legend = c("rSVD", "dashSVD", "winSVD"), pch = 16,col = c("black", "blue", "red"), horiz = T, cex = 1.2, bty = "n" )
Now let’s see how many epochs we need for rSVD, sSVD and dashSVD
to reach the accuracy of winSVD.
system.time(s1 <- rsvd::rsvd(A, k = k, q = 20)) ## the number of epochs is 4*20=40
#> user system elapsed
#> 24.976 0.158 25.165
system.time(s4 <- pcaone(A, k = k, method = "dashsvd", p = 18))
#> user system elapsed
#> 1.745 0.054 1.799
par(mar = c(5, 5, 2, 1))
plot(s0$d-s1$d, ylim = c(0, 2), xlab = "PC index", ylab = "Error of singular values", cex = 1.5, cex.lab = 2)
points(s0$d-s3$d, col = "red", cex = 1.5)
points(s0$d-s4$d, col = "blue", cex = 1.5)
legend("top", legend = c("rSVD", "dashSVD", "winSVD"), pch = 16,col = c("black", "blue", "red"), horiz = T, cex = 1.2, bty = "n" )
##
Benchmarking of speed
Let’s see the performance of pcaone compared to the other packages.
library(microbenchmark)
timing <- microbenchmark(
'RSpectra' = svds(A,k = k),
'rSVD' = rsvd(A, k=k, q = 20),
'pcaone.winsvd' = pcaone(A, k=k, p = 7),
'pcaone.dashsvd' = pcaone(A, k=k, p = 18, method = "dashsvd"),
times=10)
#> Warning in microbenchmark(RSpectra = svds(A, k = k), rSVD = rsvd(A, k = k, :
#> less accurate nanosecond times to avoid potential integer overflows
print(timing, unit='s')
#> Unit: seconds
#> expr min lq mean median uq
#> RSpectra 4.8384094 4.8984467 4.9434708 4.9301737 4.9701779
#> rSVD 24.7174787 25.1742289 25.4543530 25.3989077 25.5714469
#> pcaone.winsvd 0.8612599 0.8696085 0.8719048 0.8723306 0.8754653
#> pcaone.dashsvd 1.7654236 1.7689123 1.7858041 1.7717733 1.7844873
#> max neval
#> 5.1112929 10
#> 26.2576120 10
#> 0.8777382 10
#> 1.8411401 10