Heatmap

You probably don't understand heatmaps

• http://www.opiniomics.org/you-probably-dont-understand-heatmaps/
• Effect of number of genes

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*

• Note: Cor(X, Y) = Cor(X + constant scalar, Y). If the constant is not a scalar, the equation won't hold. Or think about plotting data in a 2 dimension space. If the X data has a constant shift for all observations/genes, then the linear correlation won't be changed.

Euclidean distance

	clustering genes	clustering samples
centering on each genes	Yes	No1
scaling on each genes	Yes	Yes2

Note

1. [math]\displaystyle{ \sum(X_i - Y_i)^2 = \sum(X_i-c_i - (Y_i-c_i))^2 }[/math]
2. [math]\displaystyle{ \sum(X_i - Y_i)^2 \neq \sum(X_i/c_i - Y_i/c_i)^2 }[/math]

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))))) # gene variance has not changed!
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, ...) genes won't affect 1-corr distance of genes.

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 after centering (no matter what measures: mean, median,...) won't affect 1-corr distance of genes.

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)))) # array variance has changed!
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

Euclidean distance and Pearson correlation relationship

http://analytictech.com/mb876/handouts/distance_and_correlation.htm. In summary,

[math]\displaystyle{ r(X, Y) = 1 - \frac{d^2(X, Y)}{2n} }[/math]

where [math]\displaystyle{ r(X, Y) }[/math] is the Pearson correlation of variables X and Y and [math]\displaystyle{ d^2(X, Y) }[/math] is the squared Euclidean distance of X and Y.

Simple image plot using image() function

https://chitchatr.wordpress.com/2010/07/01/matrix-plots-in-r-a-neat-way-to-display-three-variables/

### Create Matrix plot using colors to fill grid
# Create matrix.   Using random values for this example.
rand <- rnorm(286, 0.8, 0.3)
mat <- matrix(sort(rand), nr=26)
dim(mat)  # Check dimensions
 
# Create x and y labels
yLabels <- seq(1, 26, 1)
xLabels <- c("a", "b", "c", "d", "e", "f", "g", "h", "i",
"j", "k");
 
# Set min and max values of rand
 min <- min(rand, na.rm=T)
 max <- max(rand, na.rm=T)
 
# Red and green range from 0 to 1 while Blue ranges from 1 to 0
 ColorRamp <- rgb(seq(0.95,0.99,length=50),  # Red
                  seq(0.95,0.05,length=50),  # Green
                  seq(0.95,0.05,length=50))  # Blue
 ColorLevels <- seq(min, max, length=length(ColorRamp))
 
# Set layout.  We are going to include a colorbar next to plot.
layout(matrix(data=c(1,2), nrow=1, ncol=2), widths=c(4,1),
         heights=c(1,1))
#plotting margins.  These seem to work well for me.
par(mar = c(5,5,2.5,1), font = 2)
 
# Plot it up!
image(1:ncol(mat), 1:nrow(mat), t(mat),
     col=ColorRamp, xlab="Variable", ylab="Time",
     axes=FALSE, zlim=c(min,max),
     main= NA)
 
# Now annotate the plot
box()
axis(side = 1, at=seq(1,length(xLabels),1), labels=xLabels,
      cex.axis=1.0)
axis(side = 2, at=seq(1,length(yLabels),1), labels=yLabels, las= 1,
      cex.axis=1)
 
# Add colorbar to second plot region
par(mar = c(3,2.5,2.5,2))
 image(1, ColorLevels,
      matrix(data=ColorLevels, ncol=length(ColorLevels),nrow=1),
      col=ColorRamp,xlab="",ylab="",xaxt="n", las = 1)

If we define ColorRamp variable using the following way, we will get the 2nd plot.

require(RColorBrewer) # get brewer.pal()
ColorRamp <- colorRampPalette( rev(brewer.pal(9, "RdBu")) )(25)

Note that

• colorRampPalette() is an R's built-in function. It interpolate a set of given colors to create new color palettes. The return is a function that takes an integer argument (the required number of colors) and returns a character vector of colors (see rgb()) interpolating the given sequence (similar to heat.colors() or terrain.colors()).

# An example of showing 50 shades of grey in R
greys <- grep("^grey", colours(), value = TRUE)
length(greys)
# [1] 102
shadesOfGrey <- colorRampPalette(c("grey0", "grey100"))
shadesOfGrey(2)
# [1] "#000000" "#FFFFFF"
# And 50 shades of grey?
fiftyGreys <- shadesOfGrey(50)
mat <- matrix(rep(1:50, each = 50))
image(mat, axes = FALSE, col = fiftyGreys)
box()

• (For dual channel data) brewer.pal(9, "RdBu") creates a diverging palette based on "RdBu" with 9 colors. See help(brewer.pal, package="RColorBrewer") for a list of palette name. The meaning of the palette name can be found on colorbrew2.org website.
• (For single channel data) brewer.pal(9, "Blues") is good. See an example.

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))

Self-defined distance/linkage method

https://stackoverflow.com/questions/6806762/setting-distance-matrix-and-clustering-methods-in-heatmap-2

heatmap.2(..., hclustfun = function(x) hclust(x,method = 'ward.D2'), ...)

Change breaks in scale

https://stackoverflow.com/questions/17820143/how-to-change-heatmap-2-color-range-in-r

Con: it'll be difficult to interpret the heatmap

Color labels

https://stackoverflow.com/questions/13206335/color-labels-text-in-r-heatmap

Moving colorkey

https://stackoverflow.com/questions/15351575/moving-color-key-in-r-heatmap-2-function-of-gplots-package

White strips (artifacts)

On my Linux (Dell Precision T3500, NVIDIA GF108GL, Quadro 600, 1920x1080), the heatmap shows several white strips when I set a resolution 800x800 (see the plot of 10000 genes shown below). Note if I set a higher resolution 1920x1920, the problem is gone but the color key map will be quite large and the text font will be small.

On MacBook Pro (integrated Intel Iris Pro, 2880x1800), there is no artifact even with 800x800 resolution.

How about saving the plots using

• a different format (eg tiff) or even the lossless compression option - not help
• Cairo package - works. Note that the default background is transparent.

ggplot2 package

• https://learnr.wordpress.com/2010/01/26/ggplot2-quick-heatmap-plotting/
• http://www.kim-herzig.de/2014/06/19/heat-maps-with-ggplot2/
• http://is-r.tumblr.com/post/32387034930/simplest-possible-heatmap-with-ggplot2
• http://smartdatawithr.com/en/creating-heatmaps/#more-875 data values are shown in cells!

NMF package

aheatmap() function.

• http://nmf.r-forge.r-project.org/aheatmap.html
• http://www.gettinggeneticsdone.com/2015/04/r-user-group-recap-heatmaps-and-using.html

ComplexHeatmap

• Groups of heatmaps
• The color argument can contain a mapping function or a vector of colors. The circlize package (from the same package author) can be used.

Pros

• Annotation of classes for a new variable.

Correlation matrix

The following code will guarantee the heatmap has a diagonal in the direction of top-left and bottom-right. The row dendrogram will be flipped automatically. There is no need to use cluster_rows = rev(mydend).

mcor <- cor(t(lograt))
colnames(mcor) <- rownames(mcor) <- 1:ncol(mcor)
mydend <- as.dendrogram(hclust(as.dist(1-mcor)))
Heatmap( mcor, cluster_columns = mydend, cluster_rows = mydend,
     row_dend_reorder = FALSE, column_dend_reorder = FALSE,
     row_names_gp = gpar(fontsize = 6),
     column_names_gp = gpar(fontsize = 6),
     column_title = "", name = "value")

pheatmap

• http://wiki.bits.vib.be/index.php/Use_pheatmap_to_draw_heat_maps_in_R
• https://stackoverflow.com/questions/13087555/heatmap-in-r-how-to-resize-columns-labels

What is special? My opinions

1. the color key is thin and placed on the RHS (prettier for publications though it could miss information)
2. borders for each cell are included (not necessary)

fheatmap

(archived)

corrplot

This package is used for visualization of correlation matrix. See its vignette and Visualize correlation matrix using correlogram.

Interactive heatmaps

d3heatmap

• http://blog.rstudio.org/2015/06/24/d3heatmap/

A package generates interactive heatmaps using d3.js and htmlwidgets.

The package let you

• Highlight rows/columns by clicking axis labels
• Click and drag over colormap to zoom in (click on colormap to zoom out)
• Optional clustering and dendrograms, courtesy of base::heatmap

The following screenshots shows 3 features.

• Shows the row/column/value under the mouse cursor
• Zoom in a region (click on the zoom-in image will bring back the original heatmap)
• Highlight a row or a column (click the label of another row will highlight another row. Click the same label again will bring back the original image)

heatmaply

• http://moderndata.plot.ly/interactive-heat-maps-for-r/
• heatmaply: an R package for creating interactive cluster heatmaps for online publishing Bioinformatics 2017.

This package extends the plotly engine to heatmaps, allowing you to inspect certain values of the data matrix by hovering the mouse over a cell. You can also zoom into a region of the heatmap by drawing a rectangle over an area of your choice.

Installing this package requires to compile some dependent package.

The return object is heatmaply is 'plotly' and 'htmlwidget'. It does not return the ordering of rows/columns. It can not control whether to do clustering (d3heatmap package is better at this).

canvasXpress

• https://cran.r-project.org/web/packages/canvasXpress/index.html
• https://canvasxpress.org/html/heatmap-9.html

Dendrogram

Flip dendrogram

https://www.biostars.org/p/279775/

Color labels

• https://www.r-graph-gallery.com/dendrogram/
• 7+ ways to plot dendrograms in R
• dendrapply()

library(RColorBrewer)
# matrix contains genomics-style data where columns are samples 
#   (if otherwise remove the transposition below)
# labels is a factor variable going along the columns of matrix
plotHclustColors <- function(matrix,labels,...) {
  colnames(matrix) <- labels
  d <- dist(t(matrix))
  hc <- hclust(d, method = "ward.D2")
  labelColors <- brewer.pal(nlevels(labels),"Set1")
  colLab <- function(n) {
      if (is.leaf(n)) {
      a <- attributes(n)
      labCol <- labelColors[which(levels(labels) == a$label)]
      attr(n, "nodePar") <- c(a$nodePar, lab.col=labCol)
      }
      n
  }
  clusDendro <- dendrapply(as.dendrogram(hc), colLab)
  # I change cex because there are lots of samples
  op <- par(mar=c(5,3,1,.5)+.1, cex=.3)
  plot(clusDendro,...)
  par(op)
}

plotHclustColors(genedata, pheno)

Dendrogram with covariates

https://web.stanford.edu/~hastie/TALKS/barossa.pdf#page=41

dendextend package

Simplified from dendextend's vignette.

library(dendextend)

set.seed(1234)
iris <- datasets::iris[sample(150, 30), ] # subset for better view
iris2 <- iris[, -5] # data
species_labels <- iris[, 5] # group for coloring
 
hc_iris <- hclust(dist(iris2), method = "complete")
iris_species <- levels(species_labels)

dend <- as.dendrogram(hc_iris)
colorCodes <- c("red", "green", "blue")   
labels_colors(dend) <- colorCodes[as.numeric(species_labels)][order.dendrogram(dend)]

labels(dend) <- paste0(as.character(species_labels)[order.dendrogram(dend)],
                           "(", labels(dend), ")")
# We hang the dendrogram a bit:
dend <- hang.dendrogram(dend, hang_height=0.1)
dend <- set(dend, "labels_cex", 1.0)

png("~/Downloads/iris_dextend.png", width = 1200, height = 600)
par(mfrow=c(1,2), mar = c(3,3,1,7))
plot(dend, main = "", horiz =  TRUE)
legend("topleft", legend = iris_species, fill = colorCodes)

par(mar=c(3,1,1,5)) 
plot(as.dendrogram(hc_iris),horiz=TRUE)
dev.off()

Colors

A quick introduction to using color in density plots

http://sharpsightlabs.com/blog/quick-intro-color-density-plot/

display.brewer.pal() and brewer.pal() functions

While brewer.pal() will return colors (in hex) for a certain palette, display.brew.pal() can display the colors on a graphical device.

library(RColorBrewer)
display.brewer.pal(11, "BrBG") # Alternative colors used in correlation matrix

display.brewer.pal(9, "Set1") # Up to 9 classes are allowed

Papers

Healthcare Access and Quality Index - Lancet

http://www.thelancet.com/pdfs/journals/lancet/PIIS0140-6736(17)30818-8.pdf