Last updated: 2018-06-05

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“Uk3” is the covariance matrix corresponding to the output of the ExtremeDeconvolution algorithm that was initialized with the rank3 SVD approximation of \(X^TX\). It is the pattern of sharing identified from the dominant covariance matrix (the one with the largest mixture weight).

Here we plot the correlation matrix and the first 3 eigenvectors of “Uk3”. This provides a visualization of the primary patterns of genetic sharing identified by our method, mash. This code should closely reproduce Figure 3 of the paper.

Set up environment

First, we load a couple plotting packages used in the code chunks below.

library(lattice)
library(colorRamps)

Load data and mash results

We load some GTEx summary statistics, as well as some of the results generated from the mash analysis of the GTEx data.

covmat <- readRDS(paste("../output/MatrixEQTLSumStats.Portable.Z.coved.K3.P3",
                        "lite.single.expanded.rds",sep = "."))
pis    <- readRDS(paste("../output/MatrixEQTLSumStats.Portable.Z.coved.K3.P3",
                        "lite.single.expanded.V1.pihat.rds",sep = "."))$pihat
z.stat <- readRDS("../data/MatrixEQTLSumStats.Portable.Z.rds")$test.z
pi.mat <- matrix(pis[-length(pis)],ncol = 54,nrow = 22,byrow = TRUE)
names  <- colnames(z.stat)
colnames(pi.mat) <-
  c("ID","X'X","SVD","F1","F2","F3","F4","F5","SFA_Rank5",names,"ALL")

Compute the correlations from the \(k=3\) covariance matrix.

k        <- 3
x        <- cov2cor(covmat[[k]])
x[x < 0] <- 0

Next, we load the tissue indices and tissue names:

colnames(x) <- names
rownames(x) <- names
h <- read.table("../data/uk3rowindices.txt")[,1]

For the plots of the eigenvectors, we load the colours that are conventionally used to represent the tissues in plots.

missing.tissues <- c(7,8,19,20,24,25,31,34,37)
color.gtex <- read.table("../data/GTExColors.txt",sep = "\t",
                         comment.char = '')[-missing.tissues,]

Summarize relative importance of the covariance matrices

The posterior mixture weights give the relative importance of the covariance matrices for capturing patterns in the data.

barplot(colSums(pi.mat),las = 2,cex.names = 0.5)

Here we see that the SVD component has the largest weight.

Generate heatmap of Uk3 covariance matrix

Now we produce the heatmap showing the full covariance matrix.

smat <- (x[(h),(h)])
smat[lower.tri(smat)] <- NA
clrs <- colorRampPalette(rev(c("#D73027","#FC8D59","#FEE090","#FFFFBF",
                               "#E0F3F8","#91BFDB","#4575B4")))(64)
lat <- x[rev(h),rev(h)]
lat[lower.tri(lat)] <- NA
n <- nrow(lat)
print(levelplot(lat[n:1,],col.regions = clrs,xlab = "",ylab = "",
                colorkey = TRUE,at = seq(0,1,length.out = 64),
                scales = list(cex = 0.6,x = list(rot = 45))))

Plot eigenvectors capturing predominant patterns

The eigenvectors capture the predominant patterns in the Uk3 covariance matrix.

k <- 3
vold  <- svd(covmat[[k]])$v
u     <- svd(covmat[[k]])$u
d     <- svd(covmat[[k]])$d
v     <- vold[h,] # Shuffle so correct order
names <- names[h]
color.gtex <- color.gtex[h,]
for (j in 1:3)
  barplot(v[,j]/v[,j][which.max(abs(v[,j]))],names = "",cex.names = 0.5,
          las = 2,main = paste0("EigenVector",j,"Uk",k),
          col = as.character(color.gtex[,2]))

The first eigenvector reflects broad sharing among tissues, with all effects in the same direction; the second eigenvector captures differences between brain (and, to a less extent, testis and pituitary) vs other tissues; the third eigenvector primarily captures effects that are stronger in whole blood than elsewhere.

Session information

sessionInfo()
# R version 3.4.3 (2017-11-30)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS High Sierra 10.13.4
# 
# Matrix products: default
# BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.4/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] colorRamps_2.3  lattice_0.20-35
# 
# loaded via a namespace (and not attached):
#  [1] workflowr_1.0.1.9000 Rcpp_0.12.16         digest_0.6.15       
#  [4] rprojroot_1.3-2      R.methodsS3_1.7.1    grid_3.4.3          
#  [7] backports_1.1.2      git2r_0.21.0         magrittr_1.5        
# [10] evaluate_0.10.1      stringi_1.1.7        whisker_0.3-2       
# [13] R.oo_1.21.0          R.utils_2.6.0        rmarkdown_1.9       
# [16] tools_3.4.3          stringr_1.3.0        yaml_2.1.18         
# [19] compiler_3.4.3       htmltools_0.3.6      knitr_1.20

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