Last updated: 2020-03-08

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library(ggplot2)
Warning: package 'ggplot2' was built under R version 3.5.2
library(corrplot)
corrplot 0.84 loaded
library(softImpute)
Loading required package: Matrix
Loaded softImpute 1.4

In this script, we show that the GTEx tissue-wide gene expression data across individuals does not have a low rank factorization by looking at the eigen-values of the pairwise sample correlation matrix for a gene (PLIN1) from the GTEx genes.

We also show that imputation based models such as SoftImpute or simple median based interpolationwill fail miserably when the data contains extensive amounts of missing entries as in case of GTEx.

robocov_all_genes = get(load("/Users/kushaldey/Documents/Robocov-pages/data/Robocov_Box_all_genes.rda"))
corrplot(robocov_all_genes[,,"ENSG00000186517"],   diag = TRUE,
         col = colorRampPalette(c("lightblue4", "lightblue2", "white", "indianred1", "indianred3"))(200),
         tl.pos = "ld", tl.cex = 0.8, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "lower", tl.srt=45)

plot(eigen(as.matrix(robocov_all_genes[,,"ENSG00000186517"]))$values,
     xlab = "Features (tissues)", ylab = "Eigenvalues",
     main = "Eigenvalue trend for ARHGAP30 gene",
     col = "red",
     pch=20)

Column median imputation

dat = get(load("/Users/kushaldey/Documents/Robocov-pages/data/person_tissue_genes_voom.rda"))
gene_dat = dat[,,"ENSG00000166819"]
gene_dat_imputed = apply(gene_dat, 2, function(x) {
  y = x
  y[which(is.na(x))] = median(x[!is.na(x)])
  return(y)
})
cormat = cor(gene_dat_imputed)
corrplot(cormat,   diag = TRUE,
         col = colorRampPalette(c("lightblue4", "lightblue2", "white", "indianred1", "indianred3"))(200),
         tl.pos = "ld", tl.cex = 0.8, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "lower", tl.srt=45)

SoftImpute imputation

impute_method <- "svd"
matc=biScale(dat[,,"ENSG00000166819"],col.scale=TRUE,row.scale=FALSE,trace=TRUE)
Iter 1 Total Changes 855.6165 
Iter 2 Total Changes 10.45967 
Iter 3 Total Changes 0.3015997 
Iter 4 Total Changes 0.02422897 
Iter 5 Total Changes 0.004859336 
Iter 6 Total Changes 0.001330174 
Iter 7 Total Changes 0.0003840936 
Iter 8 Total Changes 0.0001116573 
Iter 9 Total Changes 3.246363e-05 
Iter 10 Total Changes 9.43445e-06 
Iter 11 Total Changes 2.741019e-06 
Iter 12 Total Changes 7.962422e-07 
Iter 13 Total Changes 2.312861e-07 
Iter 14 Total Changes 6.718018e-08 
Iter 15 Total Changes 1.951314e-08 
Iter 16 Total Changes 5.667748e-09 
Iter 17 Total Changes 1.646239e-09 
Iter 18 Total Changes 4.781617e-10 
fits3=softImpute(matc,rank.max=50,lambda=1,type=impute_method)
fitted_mat <- complete(dat[,,"ENSG00000166819"],fits3,unscale=T)
cormat <- cor(fitted_mat)
corrplot(cormat,   diag = TRUE,
         col = colorRampPalette(c("lightblue4", "lightblue2", "white", "indianred1", "indianred3"))(200),
         tl.pos = "ld", tl.cex = 0.8, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "lower", tl.srt=45)

impute_method <- "svd"
matc=biScale(dat[,,"ENSG00000166819"],col.scale=TRUE,row.scale=FALSE,trace=TRUE)
Iter 1 Total Changes 855.6165 
Iter 2 Total Changes 10.45967 
Iter 3 Total Changes 0.3015997 
Iter 4 Total Changes 0.02422897 
Iter 5 Total Changes 0.004859336 
Iter 6 Total Changes 0.001330174 
Iter 7 Total Changes 0.0003840936 
Iter 8 Total Changes 0.0001116573 
Iter 9 Total Changes 3.246363e-05 
Iter 10 Total Changes 9.43445e-06 
Iter 11 Total Changes 2.741019e-06 
Iter 12 Total Changes 7.962422e-07 
Iter 13 Total Changes 2.312861e-07 
Iter 14 Total Changes 6.718018e-08 
Iter 15 Total Changes 1.951314e-08 
Iter 16 Total Changes 5.667748e-09 
Iter 17 Total Changes 1.646239e-09 
Iter 18 Total Changes 4.781617e-10 
fits3=softImpute(matc,rank.max=50,lambda=1,type=impute_method)
fitted_mat <- complete(dat[,,"ENSG00000166819"],fits3,unscale=F)
cormat <- cor(fitted_mat)
corrplot(cormat,   diag = TRUE,
         col = colorRampPalette(c("lightblue4", "lightblue2", "white", "indianred1", "indianred3"))(200),
         tl.pos = "ld", tl.cex = 0.8, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "lower", tl.srt=45)

Pairwise sample correlation matrix

cormat = cor(gene_dat, use = "pairwise.complete.obs")
corrplot(cormat,   diag = TRUE,
         col = colorRampPalette(c("lightblue4", "lightblue2", "white", "indianred1", "indianred3"))(200),
         tl.pos = "ld", tl.cex = 0.8, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "lower", tl.srt=45)

Session information

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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_1.2-14  corrplot_0.84  ggplot2_3.1.1 

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.1        compiler_3.5.1    pillar_1.3.1     
 [4] git2r_0.23.0      plyr_1.8.4        workflowr_1.1.1  
 [7] R.methodsS3_1.7.1 R.utils_2.7.0     tools_3.5.1      
[10] digest_0.6.19     lattice_0.20-35   evaluate_0.12    
[13] tibble_2.1.1      gtable_0.3.0      pkgconfig_2.0.2  
[16] rlang_0.4.2       yaml_2.2.0        withr_2.1.2      
[19] stringr_1.4.0     dplyr_0.8.0.1     knitr_1.20       
[22] rprojroot_1.3-2   grid_3.5.1        tidyselect_0.2.5 
[25] glue_1.3.1        R6_2.4.0          rmarkdown_1.10   
[28] purrr_0.3.2       magrittr_1.5      whisker_0.3-2    
[31] backports_1.1.4   scales_1.0.0      htmltools_0.3.6  
[34] assertthat_0.2.1  colorspace_1.4-1  stringi_1.4.3    
[37] lazyeval_0.2.2    munsell_0.5.0     crayon_1.3.4     
[40] R.oo_1.22.0

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