\section{Heatmaps of interaction profiles}\label{heatmaps}
\subsection{Preliminaries}

<<heatmap1>>=
library(HD2013SGI)

data("Interactions",package="HD2013SGI")
data("mainEffects",package="HD2013SGI")
data("nrOfInteractionsPerTarget",package="HD2013SGI")

dir.create(file.path("result","Figures"), recursive=TRUE)
@

\subsection{Heatmap of all siRNA profiles}
$\pi$-scores for each siRNA-pair are summarized over two replicates. 
<<heatmap2>>=
PI = Interactions$piscore
for (k in seq_len(dim(PI)[5])) {
  PI[,,,,k,] = PI[,,,,k,] / Interactions$scale[k]
}
PI = (PI[,,,,,1]+PI[,,,,,2]) / 2
dim(PI) = c(prod(dim(PI)[1:2]),prod(dim(PI)[3:4]),dim(PI)[5])
dimnames(PI) = list(
  sprintf("%s_%d",rep(Interactions$Anno$target$Symbol,times=2),
          rep(seq_len(dim(Interactions$piscore)[2]),
              each=dim(Interactions$piscore)[1])),
  sprintf("%s_%d",rep(Interactions$Anno$query$Symbol,times=2),
          rep(seq_len(dim(Interactions$piscore)[4]),
              each=dim(Interactions$piscore)[3])),
  rep(dimnames(Interactions$piscore)[[5]]))
@

The color scale for interaction scores is cutted from above and below by $\pm$6. Interaction scores between -2 and 2 and colored black.
<<heatmap3>>=
cuts = c(-Inf,
         seq(-6, -2, length.out=(length(HD2013SGI:::colBY)-3)/2),
         0.0,
         seq(2, 6, length.out=(length(HD2013SGI:::colBY)-3)/2),
         +Inf)
@

A heatmap of $\pi$-scores for all siRNA pairs is plotted.
<<heatmap4,results=hide>>=
Y = PI
hcAll = HD2013SGIorderDim(Y,1)
I = hcAll$order
J = HD2013SGIorderDim(Y,2)$order
K = HD2013SGIorderDim(Y,3)$order
pdf(file=file.path("result","Figures","heatmapAll.pdf"),height=14,width=9)
HD2013SGIHeatmapHuman(x=Y[I,J,K],cuts=cuts,col=HD2013SGI:::colBY,
               colnames=TRUE,mcol=10,cexcol=0.5,mrow=0)
dev.off()
@
\begin{center}
\includegraphics[width=0.5\textwidth]{result/Figures/heatmapAll.pdf}
\end{center}

\subsection{Heatmap of best correlating siRNA profiles}
$\pi$-scores are summarized over all siRNA designs for the same gene and both replicates resulting in a single $\pi$-score per gene pair. 
<<heatmap5>>=
PI = Interactions$piscore
for (k in seq_len(dim(PI)[5])) {
  PI[,,,,k,] = PI[,,,,k,] / Interactions$scale[k]
}
PI = (PI[,,,,,1]+PI[,,,,,2]) / 2
PI = (PI[,1,,1,] + PI[,2,,1,] + PI[,1,,2,] + PI[,2,,2,])/4
@

Target genes with a minimum of 5 $\pi$-scores with $\left|\pi_{ij}\right|\ge$ 5 are selected.

<<heatmap6>>=
sel = which(nrOfInteractionsPerTarget >= 5)
PI2 = PI[sel,,]
@

Pearson correlation coefficient are computed comparing interaction profiles between all gene pairs.
<<heatmap7>>=
Y = PI2
hcAll = HD2013SGIorderDim(Y,1)
dim(Y) = c(dim(Y)[1],prod(dim(Y)[2:3]))
dimnames(Y)[[1]] = Interactions$Anno$target$Symbol[sel]
C2 = cor(t(Y),use="pairwise.complete")
@

The heatmap of correlation coefficients is plooted.
<<heatmap8,results=hide>>=
dd = as.dendrogram(hcAll)
pdf(file.path("result","Figures","heatmapSelection.pdf"))
heatmap.2(C2,col=colorRampPalette(brewer.pal(9,"RdBu"))(255),
          breaks=seq(-1,1,length.out=256),
          trace="none",Rowv=dd,Colv=dd)
dev.off()
@
\begin{center}
\includegraphics[width=0.7\textwidth]{result/Figures/heatmapSelection.pdf}
\end{center}