primepca

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Last updated: 2019-10-05

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File	Version	Author	Date	Message
Rmd	e5d8b3a	Matthew Stephens	2019-10-05	wflow_publish(“primepca.Rmd”)
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Rmd	7be583a	Matthew Stephens	2019-10-05	wflow_publish(“primepca.Rmd”)

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Introduction

I briefly experiment with primePCA package for PCA with missing data and compare its results with those from softImpute. To make the two comparable I run both with no centering (set center=FALSE in primePCA).

library("primePCA")
library("softImpute")

Loading required package: Matrix

Loaded softImpute 1.4

This first try is 50% missingness in every row, a rank 1 matrix:

set.seed(123)
n = 100
p = 200
missprob = rep(0.5,100) #make every row have 50% missing
u = rnorm(n)
v = rnorm(p)
X = u %*% t(v) + rnorm(n*p)

for(i in 1:n){
  for(j in 1:p){
    if(runif(1)<missprob[i]){X[i,j]=NA}
  }
}
res.p = primePCA(X, 1,trace.it=FALSE,center=FALSE)

Convergence threshold is hit.

res.s = softImpute(X,1)
plot(res.s$v,res.p$V_cur,main="v from primePCA vs softimpute")
abline(a=0,b=1,col=2)

Past versions of unnamed-chunk-2-1.png

Version	Author	Date
e596ca7	Matthew Stephens	2019-10-05

This is the same but missingness varies by row (uniform on 0,1).

set.seed(123)
n = 100
p = 200
missprob = runif(n) #
u = rnorm(n)
v = rnorm(p)
X = u %*% t(v) + rnorm(n*p)

for(i in 1:n){
  for(j in 1:p){
    if(runif(1)<missprob[i]){X[i,j]=NA}
  }
}
res.p = primePCA(X, 1,trace.it=FALSE,center=FALSE)

Convergence threshold is hit.

res.s = softImpute(X,1)
plot(res.s$v,res.p$V_cur,main="v from primePCA vs softimpute")
abline(a=0,b=-1,col=2)

Past versions of unnamed-chunk-3-1.png

Version	Author	Date
e596ca7	Matthew Stephens	2019-10-05

This example has higher missingness (0.8,1)

set.seed(123)
n = 100
p = 200
missprob = 0.8+ 0.2*runif(n) #at least 80% missing
u = rnorm(n)
v = rnorm(p)
X = u %*% t(v) + rnorm(n*p)

for(i in 1:n){
  for(j in 1:p){
    if(runif(1)<missprob[i]){X[i,j]=NA}
  }
}
res.p = primePCA(X, 1,trace.it=FALSE,center=FALSE)

Max iteration number is hit.

res.s = softImpute(X,1)
plot(res.s$v,res.p$V_cur,main="v from primePCA vs softimpute")
abline(a=0,b=-1,col=2)

Past versions of unnamed-chunk-4-1.png

Version	Author	Date
e596ca7	Matthew Stephens	2019-10-05

cor(cbind(v,res.p$V_cur,res.s$v))

           v                      
v  1.0000000 -0.9011763  0.9083774
  -0.9011763  1.0000000 -0.9911967
   0.9083774 -0.9911967  1.0000000

…and higher missingness again, (0.9,1). (I increased n so that every column has sufficient non-missing entries):

set.seed(123)
n = 1000
p = 200
missprob = 0.9+ 0.1*runif(n) #at least 90% missing
u = rnorm(n)
v = rnorm(p)
X = u %*% t(v) + rnorm(n*p)

for(i in 1:n){
  for(j in 1:p){
    if(runif(1)<missprob[i]){X[i,j]=NA}
  }
}
res.p = primePCA(X, 1,trace.it=FALSE,center=FALSE)

Max iteration number is hit.

res.s = softImpute(X,1)
plot(res.s$v,res.p$V_cur,main="v from primePCA vs softimpute")
abline(a=0,b=-1,col=2)

Past versions of unnamed-chunk-5-1.png

Version	Author	Date
e596ca7	Matthew Stephens	2019-10-05

cor(cbind(v,res.p$V_cur,res.s$v))

           v                      
v  1.0000000  0.9878358 -0.9867028
   0.9878358  1.0000000 -0.9983583
  -0.9867028 -0.9983583  1.0000000

Interestingly, the results from trace.it=FALSE in primePCA suggest it is maybe entering an infinite loop in this case. I guess that maybe this is probably because of changes in the rows selected, and indeed was able to avoid it by setting very large thresh_sigma=1e100. (In this case it appears to just filter out the rows with only one entry; in the other case it sometimes filters out one additional row).

Session information

sessionInfo()

R version 3.6.0 (2019-04-26)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Mojave 10.14.4

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] softImpute_1.4 Matrix_1.2-17  primePCA_1.0  

loaded via a namespace (and not attached):
 [1] workflowr_1.4.0 Rcpp_1.0.2      lattice_0.20-38 digest_0.6.20  
 [5] rprojroot_1.3-2 MASS_7.3-51.4   grid_3.6.0      backports_1.1.4
 [9] git2r_0.26.1    magrittr_1.5    evaluate_0.14   stringi_1.4.3  
[13] fs_1.3.1        whisker_0.3-2   rmarkdown_1.14  tools_3.6.0    
[17] stringr_1.4.0   glue_1.3.1      xfun_0.8        yaml_2.2.0     
[21] compiler_3.6.0  htmltools_0.3.6 knitr_1.23