Z-Score calculation by heatmap.2

Question

[Chirag Parsania]

I have generated 2 heatmaps using heatmap.2 function. Following is my command and it's output. First heatmap contains z-score which is been calculated by heatmap.2 function with parameter "scale=row". While second heatmap I have generated is with values calculated by my own function name "normalisation" which also calculate the Z-score. Surprisingly output is different in both case. I wonder how heatmap.2 calculate the Z-Score. The way I have calculated Z-score is right ? Please help.

Command For First Heatmap --> h1

heatmap.2 (
mat ,

    col=colorRampPalette(c("blue","white","red"))(dim(mat)[1]*dim(mat)[2]),
    density ="none",
    Colv = T,
    Rowv=T,
    trace ="none",
    scale="row",
    dendrogram = "both",
    main = paste("Cg_Pol_2_Top_2k_Highly_Variable"),#,dim(mat)[1],sep =" "),
    adjCol = c(1,0),
    margins = c(10,4),
    lmat =  rbind(c(4,3),c(2,1)), 
    lwid = c(1.5,4), 
    lhei = c(0.5,5),
    labRow=c(""),
    keysize=1,

  )

Command for heatmap 2

heatmap.2 (
normalisation(mat),

    col=colorRampPalette(c("blue","white","red"))(dim(mat)[1]*dim(mat)[2]),
    density ="none",
    Colv = T,
    Rowv=T,
    trace ="none",
    scale="none",
    dendrogram = "both",
    main = paste("Cg_Pol_2_Top_2k_Highly_Variable"),#,dim(mat)[1],sep =" "),
    adjCol = c(1,0),
    margins = c(10,4),
    lmat =  rbind(c(4,3),c(2,1)), 
    lwid = c(1.5,4), 
    lhei = c(0.5,5),
    labRow=c(""),
    keysize=1,

  )

normalization<-function(x){
  dimm=dim(x)
  for(i in 1:dimm[1]){
    x[i,]=(x[i,]-mean(x[i,]))/sd(x[i,]) 
  }
  return(x)
}

[Carlo Yague]

You use normalisation(mat) and not normaliZation(mat) in your code. Is it a typo or could "normalisation" be a different function than the one written below ?

Answer 1

[Kevin Blighe]

Better late than never...

The actual code snippet from heatmap.2 is:

if (scale == "row") {
    retval$rowMeans <- rm <- rowMeans(x, na.rm = na.rm)
    x <- sweep(x, 1, rm)
    retval$rowSDs <- sx <- apply(x, 1, sd, na.rm = na.rm)
    x <- sweep(x, 1, sx, "/")
}
else if (scale == "column") {
    retval$colMeans <- rm <- colMeans(x, na.rm = na.rm)
    x <- sweep(x, 2, rm)
    retval$colSDs <- sx <- apply(x, 2, sd, na.rm = na.rm)
    x <- sweep(x, 2, sx, "/")
}

The standard way to scale (by column) to the Z-scale in R is with the scale function, i.e., subtract the mean and then divide by the standard deviation [of each column] - to do this by row, which is typically related to genes, we would transpose the data, apply scale(), and then transpose back (t(scale(t(x)))), which is ultimately the same as what is happening in the heatmap.2 code. The proof:

generate random matrix of numbers

mat <- matrix(rexp(200, rate=.1), ncol=20)

heatmap.2 functions

na.rm <- TRUE
scaleRow <- function(x) {
        rm <- rowMeans(x, na.rm = na.rm)
        x <- sweep(x, 1, rm)
        sx <- apply(x, 1, sd, na.rm = na.rm)
        x <- sweep(x, 1, sx, "/")
        return(round(x, 6))
}
scaleCol <- function(x) {
        colMeans <- rm <- colMeans(x, na.rm = na.rm)
        x <- sweep(x, 2, rm)
        colSDs <- sx <- apply(x, 2, sd, na.rm = na.rm)
        x <- sweep(x, 2, sx, "/")
        return(round(x, 6))
}

check that heatmap.2 functions produce same data as manually using scale()

all((scaleRow(mat) == round(t(scale(t(mat))), 6)) == TRUE)
[1] TRUE

all((scaleCol(mat) == round(scale(mat), 6)) == TRUE)
[1] TRUE

Kevin