Heatmap

Evaluate the effect of centering & scaling

1-correlation distance

Effect of centering and scaling on clustering of genes and samples in terms of distance. 'Yes' means the distance was changed compared to the baseline where no centering or scaling was applied.

	clustering genes	clustering samples
centering on each genes	No	Yes
scaling on each genes	No	Yes

Euclidean distance

	clustering genes	clustering samples
centering on each genes	Yes	No
scaling on each genes	Yes	Yes

Supporting R code

1. 1-Corr distance

source("http://www.bioconductor.org/biocLite.R")
biocLite("limma"); biocLite("ALL")

library(limma); library(ALL)
data(ALL)

eset <- ALL[, ALL$mol.biol %in% c("BCR/ABL", "ALL1/AF4")]

f <- factor(as.character(eset$mol.biol))
design <- model.matrix(~f)
fit <- eBayes(lmFit(eset,design))
selected  <- p.adjust(fit$p.value[, 2]) < 0.05
esetSel <- eset [selected, ]   # 165 x 47
heatmap(exprs(esetSel))

esetSel2 <- esetSel[sample(1:nrow(esetSel), 20), sample(1:ncol(esetSel), 10)] # 20 x 10

dist.no <- 1-cor(t(as.matrix(esetSel2))) 
dist.mean <- 1-cor(t(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)))))
dist.median <- 1-cor(t(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median))))

range(dist.no - dist.mean) # [1] -1.110223e-16  0.000000e+00
range(dist.no - dist.median) # [1] -1.110223e-16  0.000000e+00
range(dist.mean - dist.median) # [1] 0 0

So centering (no matter which measure: mean, median, ...), it won't affect 1-corr distance.

dist.mean <- 1-cor(t(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)), "/")))
dist.median <- 1-cor(t(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median), "/")))
range(dist.no - dist.mean) # [1] -8.881784e-16  6.661338e-16
range(dist.no - dist.median) # [1] -6.661338e-16  6.661338e-16
range(dist.mean - dist.median) # [1] -1.110223e-15  1.554312e-15

So scaling (no matter what measures: mean, median,...), it won't affect 1-corr distance.

How about centering / scaling genes on array clustering?

dist.no <- 1-cor(as.matrix(esetSel2))
dist.mean <- 1-cor(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2))))
dist.median <- 1-cor(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median)))

range(dist.no - dist.mean) # [1] -1.547086  0.000000
range(dist.no - dist.median) # [1] -1.483427  0.000000
range(dist.mean - dist.median) # [1] -0.5283601  0.6164602

dist.mean <- 1-cor(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)), "/"))
dist.median <- 1-cor(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median), "/"))
range(dist.no - dist.mean) # [1] -1.477407  0.000000
range(dist.no - dist.median) # [1] -1.349419  0.000000
range(dist.mean - dist.median) # [1] -0.5419534  0.6269875

2. Euclidean distance

dist.no <- dist(as.matrix(esetSel2))
dist.mean <- dist(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2))))
dist.median <- dist(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median)))

range(dist.no - dist.mean) # [1] 7.198864e-05 2.193487e+01
range(dist.no - dist.median) # [1] -0.3715231 21.9320846
range(dist.mean - dist.median) # [1] -0.923717629 -0.000088385

Centering does affect the Euclidean distance.

dist.mean <- dist(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)), "/"))
dist.median <- dist(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median), "/"))

range(dist.no - dist.mean) # [1]  0.7005071 24.0698991
range(dist.no - dist.median) # [1]  0.636749 24.068920
range(dist.mean - dist.median) # [1] -0.22122869  0.02906131

And scaling affects Euclidean distance too.

How about centering / scaling genes on array clustering?

dist.no <- dist(t(as.matrix(esetSel2)))
dist.mean <- dist(t(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)))))
dist.median <- dist(t(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median))))

range(dist.no - dist.mean) # 0 0
range(dist.no - dist.median)  # 0 0
range(dist.mean - dist.median) # 0 0

dist.mean <- dist(t(sweep(as.matrix(esetSel2), 1L, rowMeans(as.matrix(esetSel2)), "/")))
dist.median <- dist(t(sweep(as.matrix(esetSel2), 1L, apply(esetSel2, 1, median), "/")))

range(dist.no - dist.mean) # [1] 1.698960 9.383789
range(dist.no - dist.median)  # [1] 1.683028 9.311603
range(dist.mean - dist.median) # [1] -0.09139173  0.02546394

gplots package

The following example is extracted from DESeq2 package.

## ----loadDESeq2, echo=FALSE----------------------------------------------
# in order to print version number below
library("DESeq2")

## ----loadExonsByGene, echo=FALSE-----------------------------------------
library("parathyroidSE")
library("GenomicFeatures")
data(exonsByGene)

## ----locateFiles, echo=FALSE---------------------------------------------
bamDir <- system.file("extdata",package="parathyroidSE",mustWork=TRUE)
fls <- list.files(bamDir, pattern="bam$",full=TRUE)


## ----bamfilepaired-------------------------------------------------------
library( "Rsamtools" )
bamLst <- BamFileList( fls, yieldSize=100000 )


## ----sumOver-------------------------------------------------------------
library( "GenomicAlignments" )
se <- summarizeOverlaps( exonsByGene, bamLst,
                         mode="Union",
                         singleEnd=FALSE,
                         ignore.strand=TRUE,
                         fragments=TRUE )

## ----libraries-----------------------------------------------------------
library( "DESeq2" )
library( "parathyroidSE" )

## ----loadEcs-------------------------------------------------------------
data( "parathyroidGenesSE" )
se <- parathyroidGenesSE
colnames(se) <- se$run

## ----fromSE--------------------------------------------------------------
ddsFull <- DESeqDataSet( se, design = ~ patient + treatment )

## ----collapse------------------------------------------------------------
ddsCollapsed <- collapseReplicates( ddsFull,
                                    groupby = ddsFull$sample, 
                                    run = ddsFull$run )

## ----subsetCols----------------------------------------------------------
dds <- ddsCollapsed[ , ddsCollapsed$time == "48h" ]

## ----subsetRows, echo=FALSE----------------------------------------------
idx <- which(rowSums(counts(dds)) > 0)[1:4000]
dds <- dds[idx,]

## ----runDESeq, cache=TRUE------------------------------------------------
dds <- DESeq(dds)

rld <- rlog( dds)

library( "genefilter" )
topVarGenes <- head( order( rowVars( assay(rld) ), decreasing=TRUE ), 35 )

## ----beginner_geneHeatmap, fig.width=9, fig.height=9---------------------
library(RColorBrewer)
library(gplots)
heatmap.2( assay(rld)[ topVarGenes, ], scale="row", 
           trace="none", dendrogram="column", 
           col = colorRampPalette( rev(brewer.pal(9, "RdBu")) )(255))