Table of Contents
Quantile normalization is a data pre-processing technique used to standardize the data distribution of multiple datasets. It can be performed in R by first loading the datasets into R, then using the quantile function to calculate the quantiles of the datasets, and finally using the scale function to normalize the datasets to the same distribution. The final step is to use the match function to match the distributions to each other.
In statistics, is a method that makes two distributions identical in statistical properties.
The following example shows how to perform quantile normalization in R.
Example: Quantile Normalization in R
Suppose we create the following data frame in R that contains two columns:
#make this example reproducible set.seed(0) #create data frame with two columns df <- data.frame(x=rnorm(1000), y=rnorm(1000)) #view first six rows of data frame head(df) x y 1 1.2629543 -0.28685156 2 -0.3262334 1.84110689 3 1.3297993 -0.15676431 4 1.2724293 -1.38980264 5 0.4146414 -1.47310399 6 -1.5399500 -0.06951893
We can use the and functions to calculate the quantiles for both x and y:
#calculate quantiles for x and y
sapply(df, function(x) quantile(x, probs = seq(0, 1, 1/4)))
x y
0% -3.23638573 -3.04536393
25% -0.70845589 -0.73331907
50% -0.05887078 -0.03181533
75% 0.68763873 0.71755969
100% 3.26641452 3.03903341
Notice that x and y have similar values for the quantiles, but not identical values.
For example, the value at the 25th percentile for x is -0.708 and the value at the 25th percentile for y is -0.7333.
To perform quantile normalization, we can use the normalize.quantiles() function from the package in R:
library(preprocessCore) #perform quantile normalization df_norm <- as.data.frame(normalize.quantiles(as.matrix(df))) #rename data frame columns names(df_norm) <- c('x', 'y') #view first six row of new data frame head(df_norm) x y 1 1.2632137 -0.28520228 2 -0.3469744 1.82440519 3 1.3465807 -0.16471644 4 1.2692599 -1.34472394 5 0.4161133 -1.43717759 6 -1.6269731 -0.07906793
We can then use the following code to calculate the quantiles for both x and y again:
#calculate quantiles for x and y
sapply(df_norm, function(x) quantile(x, probs = seq(0, 1, 1/4)))
x y
0% -3.14087483 -3.14087483
25% -0.72088748 -0.72088748
50% -0.04534305 -0.04534305
75% 0.70259921 0.70259921
100% 3.15272396 3.15272396
Notice that the quantiles are identical for x and y now.
We would say that x and y have been quantile normalized. That is, the two distributions are now identical in statistical properties.
The following tutorials explain how to perform other common tasks in R: