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# Additional File 1
# for "Principal component analysis for designed experiments". 
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## Importing your matrix data into R (in this demonstration, a matrix available from GEO is used)
	masterdata<-read.table(file="GSE31291_Summarized_Matrix.txt", sep="\t", header=T)
	masterdata <- masterdata[, 1:40*3+1]
	rownames(masterdata)<-masterdata[,1]
	colnames(masterdata)<-colnames(masterdata)[ 1:40*3-1]
	masterdata<- as.matrix(masterdata)
	(masterdata[1:10,] )

## ANOVA
	ANOVA_negatives <- NA   #  In fact, many of the genes were negative.
    	  # Here, this demonstration will represent Figure 1C;
    	  # hence, for comparison, it will use ANOVA negative genes as well. 
    	  # However, in practice, such genes should be removed to reduce the noise effects.

## Preparing the training_data 
	num_sample 	<- 	ncol(masterdata)
	num_gene 	<- 	nrow(masterdata)
	num_repeat 	<- 	4  # number of each repeat

	training<-array(NA, dim=c(num_gene, num_sample/num_repeat))

		for(gene in 1:num_gene){
		for(group in 1:(num_sample/num_repeat)){
		training[gene,group]<- mean(masterdata[gene, 1:num_repeat+(group-1)*num_repeat], na.rm=T)
		}}

	rownames(training)<-masterdata[,1]
	colnames(training)<- 0:9

## Centering
	center <- apply(training, 1, mean, na.rm=T)   	# setting the mean data as the reference
	# center <- training[,1]			# alternative: 0h as the reference
	X <- sweep(training, 1, center)
	X <- t(X)    # transpose of X 
	X_c <- sweep(masterdata, 1, center) # complete data
	X_c <- t(X_c)    

##  Removing NAs (and ANOVA negatives)
	X[is.na(X)]<-0
	 X[ ,ANOVA_negatives] <- 0 # removing noisy items by replacing the data with zero
	X_c[is.na(X_c)]<-0
	 X_c[ ,ANOVA_negatives]<-0 

## SVD
	#  singular value decomposition of X  
		res_svd <- svd(X)
			Left <- res_svd$u		# the left singular vectors
			Right <- res_svd$v		# the right singular vectors
			sqL <- diag(res_svd$d)		# diagonal matrix of the singular values

 	#  calculation of the principal components 
	  PC_gene  	<-	t(X) %*% Left		#/ Right %*% sqL
	  PC_groups	<-	X %*% Right		#/ Left %*% sqL
	  PC_all_samples <- 	X_c %*% Right 		# applying the axes to other data sets
	  proportion <- res_svd$d^2/sum(res_svd$d^2)*100	# proportion of characteristic roots

	# scaling of the principal components 
	  sPC_gene <- PC_gene /sqrt( nrow(X) )
	  sPC_groups <- PC_groups / sqrt( ncol(X) )
	  sPC_all_samples <- PC_all_samples / sqrt( ncol(X))   

### Presentation of sPC1 and sPC2
	#  barplot(proportion)
		groups<- sort(rep(0:9,4))
	plot(sPC_gene[,1], sPC_gene[,2]   )  # , pch=NA, xlim=c(-.25,.25), ylim=c(-.25,.25))
	text(sPC_all_samples[,1], sPC_all_samples[,2], labels=groups, col="green2")

## Exporting the resulted PCs
	write.table(sPC_all_samples, file="PC_samples.txt", sep="\t")
	write.table(sPC_groups, file="PC_groups.txt", sep="\t")
	write.table(sPC_gene, file="PC_gene.txt", sep="\t")

## Tomokazu Konishi, 5 Oct 2011, konishi@akita-pu.ac.jp