# Nonlinear Scaling Normalization

I have a procedure for normalizing variables, the details of which can be viewed in this white paper.

I would like to be able to make the routine scalable to handle any number of variables. Below is the R code for a 4 variable example with a regular correlation coefficient substituted for the preferred nonlinear coefficient (for simplicity and demonstration purposes). Any insights or comments are appreciated.

VN_Normalization <- function(A1, A2, A3, A4){

#Array1 Scaling Factor
RG_Factor_A1_A2<- mean(A1)/mean(A2)
RG_Factor_A1_A3<- mean(A1)/mean(A3)
RG_Factor_A1_A4<- mean(A1)/mean(A4)

#Array2 Scaling Factor
RG_Factor_A2_A1<- mean(A2)/mean(A1)
RG_Factor_A2_A3<- mean(A2)/mean(A3)
RG_Factor_A2_A4<- mean(A2)/mean(A4)

#Array3 Scaling Factor
RG_Factor_A3_A1<- mean(A3)/mean(A1)
RG_Factor_A3_A2<- mean(A3)/mean(A2)
RG_Factor_A3_A4<- mean(A3)/mean(A4)

#Array4 Scaling Factor
RG_Factor_A4_A1<- mean(A4)/mean(A1)
RG_Factor_A4_A2<- mean(A4)/mean(A2)
RG_Factor_A4_A3<- mean(A4)/mean(A3)

#A1 as Reference Gene
A1_1 <- A1
A2_1 <- A2*RG_Factor_A1_A2*abs((cor(A1,A2)))
A3_1 <- A3*RG_Factor_A1_A3*abs((cor(A1,A3)))
A4_1 <- A4*RG_Factor_A1_A4*abs((cor(A1,A4)))

#A2 as Reference Gene
A1_2 <- A1*RG_Factor_A2_A1*abs((cor(A1,A2)))
A2_2 <- A2
A3_2 <- A3*RG_Factor_A2_A3*abs((cor(A2,A3)))
A4_2 <- A4*RG_Factor_A2_A4*abs((cor(A2,A4)))

#A3 as Reference Gene
A1_3 <- A1*RG_Factor_A3_A1*abs((cor(A1,A3)))
A2_3 <- A2*RG_Factor_A3_A2*abs((cor(A3,A2)))
A3_3 <- A3
A4_3 <- A4*RG_Factor_A3_A4*abs((cor(A3,A4)))

#A4 as Reference Gene
A1_4 <- A1*RG_Factor_A4_A1*abs((cor(A1,A4)))
A2_4 <- A2*RG_Factor_A4_A2*abs((cor(A4,A2)))
A3_4 <- A3*RG_Factor_A4_A3*abs((cor(A4,A3)))
A4_4 <- A4

A1_Normalized <- (A1_1+A1_2+A1_3+A1_4)/4
A2_Normalized <- (A2_1+A2_2+A2_3+A2_4)/4
A3_Normalized <- (A3_1+A3_2+A3_3+A3_4)/4
A4_Normalized <- (A4_1+A4_2+A4_3+A4_4)/4

p = sample(rainbow(10))
boxplot(list(A1,A2,A3,A4,A1_Normalized,A2_Normalized,A3_Normalized,A4_Normalized),
las=2, names=c("Array1","Array2","Array3","Array4",
"Array1_Normalized","Array2_Normalized","Array3_Normalized","Array4_Normalized"),
col=c("white","white","white","white",p,p,p,p))

}


I feel the key to generalizing your code is to store your variables into a matrix. Then let vectorized functions (colMeans, cor, *, etc.) do their magic:

A <- cbind(A1, A2, A3, A4)

VN_Normalization <- function(A) {
m  <- colMeans(A)
RG <- m %o% (1/m)
scales <- colMeans(RG * abs(cor(A)))
A_Normalized <- t(t(A) * scales)

n <- ncol(A)
i <- seq_len(n)
labels <- c(sprintf("Array%i", i),
sprintf("Array%i_Normalized", i))
boxplot(cbind(A, A_Normalized),
las = 2, names = labels,
col = c(rep("white", n), rainbow(n)))
}


Please let me know if I missed anything (I assumed A1, A2, etc. were numeric vectors of equal lengths.)

• Thanks @flodel, you did not miss anything as that was a valid assumption! Is there a way to store the normalized variables as global variables using the colnames(A)[i] and then pasting _Normalized to the result? For example if A<- cbind(SPY,TLT) I'd like to store SPY_Normalized and TLT_Normalized. I tried this paste(colnames(A)[i], "_Normalized", sep="") <<- A_Normalized[,i] without success. May 1, 2015 at 13:42
• To answer your exact request, you would need to use the assign function. Later, you would need to use get to access e.g. SNP_Normalized given X <- "SNP": get(paste(X, "Normalized", sep = "_")). This is a really bad approach for many, many reasons. The right way to do things is to keep all your normalized variables in a matrix as well (or a list or a data.frame if you want to modify the code a little). Just add return(A_Normalized) at the end of the function. Call the function as follows: Normalized <- VN_Normalization(A). Then, you will be able to access Normalized[, X]. May 2, 2015 at 11:15