Steve’s Data Tips and Tricks - Mastering Quantile Normalization in R: A Step-by-Step Guide (2024)

Step 1: Load Your Data

First things first, you’ll need some data to work with. For the sake of this tutorial, let’s say you have a dataframe called df containing your datasets.

set.seed(42) # For reproducibilitydf <- data.frame( sample1 = rnorm(100, mean = 5, sd = 2), sample2 = rnorm(100, mean = 10, sd = 1), sample3 = rnorm(100))head(df)

 sample1 sample2 sample31 7.741917 11.200965 -2.00092922 3.870604 11.044751 0.33377723 5.726257 8.996791 1.17132514 6.265725 11.848482 2.05953925 5.808537 9.333227 -1.37686166 4.787751 10.105514 -1.1508556

hist(df$sample1, col = 'red', xlim=c(min(df), max(df)),  main = 'Distribution of Sample 1')hist(df$sample2, col = 'blue', add = TRUE)hist(df$sample3, col = 'green', add = TRUE)#add legendlegend('topright',  c('Sample 1', 'Sample 2','Sample 3'),  fill=c('red','blue', 'green'))

Step 2: Perform Quantile Normalization

Now, it’s time to perform quantile normalization using R’s built-in quantile() function. This function calculates quantiles for a given dataset, which is essential for aligning the distributions. Function from: https://lifewithdata.com/2023/09/02/how-to-perform-quantile-normalization-in-r/

# Perform quantile normalizationqn <- function(.data){ data_sort <- apply(.data, 2, sort) row_means <- rowMeans(data_sort) data_sort <- matrix(row_means,  nrow = nrow(data_sort),  ncol = ncol(data_sort),  byrow = TRUE ) index_rank <- apply(.data, 2, order) normalized_data <- matrix(nrow = nrow(.data), ncol = ncol(.data)) for(i in 1:ncol(.data)){ normalized_data[,i] <- data_sort[index_rank[,i], i] } return(normalized_data)}normalized_data <- qn(df)

Let’s break down this code snippet:

Absolutely, let’s break down this R code block piece by piece:

1. Function Definition:

qn <- function(.data){ # ... function body here ...}

This defines a function named qn that takes a data frame (data) as input. This data frame is most likely your dataset you want to normalize.

2. Sorting Each Column:

data_sort <- apply(.data, 2, sort)

This line sorts each column of the data frame data independently. Imagine sorting rows of data like sorting words in a dictionary. Here, we are sorting each column (each variable) from smallest to largest values. The result is stored in data_sort.

3. Calculating Row Means:

row_means <- rowMeans(data_sort)

This line calculates the average value for each row in the sorted data frame (data_sort). So, for each row (each data point), it finds the mean of the sorted values across all variables. The result is stored in row_means.

4. Replicating Row Means into a Matrix:

data_sort <- matrix(row_means,  nrow = nrow(data_sort),  ncol = ncol(data_sort),  byrow = TRUE )

This part is a bit trickier. It creates a new matrix (data_sort) with the same dimensions (number of rows and columns) as the original sorted data. Then, it fills each row of this new matrix with the corresponding row mean calculated earlier (row_means). The byrow argument ensures this replication happens row-wise.

5. Ranking Each Value’s Position:

index_rank <- apply(.data, 2, order)

Similar to sorting, this line assigns a rank (position) to each value within its column (variable) in the original data frame (data). Imagine a race where the first place gets rank 1, second place gets rank 2, and so on. Here, the rank indicates the original position of each value after everything was sorted in step 2. The result is stored in index_rank.

6. Building the Normalized Data Frame:

normalized_data <- matrix(nrow = nrow(.data), ncol = ncol(.data))

This line creates an empty matrix (normalized_data) with the same dimensions as the original data frame. This will eventually hold the normalized data.

7. Looping Through Columns and Assigning Ranked Values:

for(i in 1:ncol(.data)){ normalized_data[,i] <- data_sort[index_rank[,i], i]}

This is the core of the normalization process. It loops through each column (variable) of the original data frame (data). For each column, it uses the ranks (index_rank) as indices to pick values from the sorted data with row means (data_sort). Basically, it replaces each value in the original data with the value from the sorted data that has the same rank (original position). This effectively replaces the original values with their corresponding row means (representing the center point) based on their original order.

8. Returning the Normalized Data:

return(normalized_data)

Finally, the function returns the normalized_data matrix, which contains the quantile normalized version of your original data frame.

In essence, this code performs a type of rank-based normalization where each value is replaced with the row mean that corresponds to its original position after sorting all the data together. This approach ensures that the distribution of values across columns becomes more consistent.

Step 3: Explore the Results

After quantile normalization, you’ll have a list of normalized datasets ready for further analysis. Take a moment to explore the results and ensure that the distributions are aligned as expected.

summary(df)

 sample1 sample2 sample3 Min. :-0.9862 Min. : 7.975 Min. :-2.69993 1st Qu.: 3.7666 1st Qu.: 9.409 1st Qu.:-0.71167 Median : 5.1796 Median : 9.931 Median :-0.02474 Mean : 5.0650 Mean : 9.913 Mean :-0.01037 3rd Qu.: 6.3231 3rd Qu.:10.462 3rd Qu.: 0.65254 Max. : 9.5733 Max. :12.702 Max. : 2.45959 

# Explore the resultssummary(normalized_data)

 V1 V2 V3 Min. :1.430 Min. :1.430 Min. :1.430 1st Qu.:4.154 1st Qu.:4.154 1st Qu.:4.154 Median :5.029 Median :5.029 Median :5.029 Mean :4.989 Mean :4.989 Mean :4.989 3rd Qu.:5.812 3rd Qu.:5.812 3rd Qu.:5.812 Max. :8.245 Max. :8.245 Max. :8.245 

Step 4: Obtain Quantiles

Now that the data is normalized, we can extract the quantiles to compare the distributions across datasets. This will help you confirm that the normalization process was successful.

as.data.frame(normalized_data) |>  sapply(function(x) quantile(x, probs = seq(0,1,1/4)))

 V1 V2 V30% 1.429737 1.429737 1.42973725% 4.154481 4.154481 4.15448150% 5.028521 5.028521 5.02852175% 5.812480 5.812480 5.812480100% 8.244925 8.244925 8.244925

As we can see, the quantiles of the normalized data are consistent across the different datasets. This indicates that the distributions have been aligned through quantile normalization.

Let’s visuzlize for another confirmation

df_normalized <- as.data.frame(normalized_data)hist(df_normalized$V1, col = 'red')hist(df_normalized$V2, col = 'blue', add = TRUE)hist(df_normalized$V3, col = 'green', add = TRUE)legend('topright', c('Sample 1', 'Sample 2','Sample 3'), fill=c('red','blue', 'green'))