How to Normalize and Standardize Data in R?

In this article, we will be looking at the various techniques to scale data,  Min-Max Normalization, Z-Score Standardization, and Log Transformation in the R programming language.

Loading required packages and dataset:

Let’s install and load the required packages. And also create a dataframe as a sample dataset.

R

# load packages and data
install.packages("caret")
library(caret)

# creating a dataset
data = data.frame(var1=c(120, 345, 145, 122, 596, 285, 211),
                  var2=c(10, 15, 45, 22, 53, 28, 12),
                  var3=c(-34, 0.05, 0.15, 0.12, -6, 0.85, 0.11))

data

Output:

Summary of Data:

Let’s check out the summary of the data before scaling it. As we can see from the output, each variable/feature has a different range of values (which can be inferred from min and max values) and thus need scaling to bring the values within a fixed range.

R

# import the library
library(caret)

# creating the dataset
data = data.frame(var1 = c(120,345,145,122,596,285,211),
           var2 = c(10,15,45,22,53,28,12),
           var3 = c(-34,0.05,0.15,0.12,-6,0.85,0.11))

# summary of data
summary(data)

Output:

Normalization:

Method 1: Min-Max Normalization

This technique rescales values to be in the range between 0 and 1. Also, the data ends up with smaller standard deviations, which can suppress the effect of outliers.

Example: Let’s write a custom function to implement Min-Max Normalization. 

 Min-Max Normalization

This is the formula for Min-Max Normalization. Let’s use this formula and create a custom user-defined function, minMax which takes in one value at a time and computes the scaled value such that it lies between 0 and 1. Here new_max(A) is 1 and new_min(A) is 0 as we trying in scale down/up the values in the range [0,1].

This helps in handling the outliers well and suppresses them overall. 

R

# import the library
library(caret)

# dataset
data = data.frame(var1 = c(120,345,145,122,596,285,211),
           var2 = c(10,15,45,22,53,28,12),
           var3 = c(-34,0.05,0.15,0.12,-6,0.85,0.11))

# custom function to implement min max scaling
minMax <- function(x) {
  (x - min(x)) / (max(x) - min(x))
}

#normalise data using custom function
normalisedMydata <- as.data.frame(lapply(data, minMax))
head(normalisedMydata)

Output:

Let’s now check if the values of the 4 columns are rescaled between 0 and 1 using a summary of the data (min and max are 0 and 1 respectively).

R

# checking summary after normalization
summary(normalisedMydata)

Output:

Example: Using an in-built function and caret package to perform Min-Max Normalization 

Here the method, preProcess( ) takes a tuple with value “range” to implement min-max scaling and this preprocessed data is sent to predict( ) function to get the final normalized data using the min-max scaling method.  

Syntax:

preProcess(x, method = c(“center”, “scale”), … na.remove = TRUE )

Arguments:

• x – a matrix or data frame
• method – a character vector specifying the type of processing
• na.remove – true/false to specify removal of missing values

R

# import the library
library(caret)

# dataset
data = data.frame(var1 = c(120,345,145,122,596,285,211),
           var2 = c(10,15,45,22,53,28,12),
           var3 = c(-34,0.05,0.15,0.12,-6,0.85,0.11))

# preprocess the data
preproc <- preProcess(mydata, method=c("range"))

# perform normalization
norm <- predict(preproc, mydata)
head(norm)

Output:

This technique tends to center the rescaled data around the mean, but it doesn’t handle outliers very well. So to tackle this we go for standardization.

Method 2: Log Transformation

Not all real-life data would follow a gaussian distribution nor would be less skewed. So to tackle this Log Transformation technique can be used.

Example: Using log( ) function

Let’s log transform a particular column var2 in data and view it’s summary.

Syntax:

log(x, base = exp(1))

Arguments:

• x – a numeric or complex vector
• base – a positive or complex number

Log( ) function takes in numeric vector or complex vector of the data and performs log transformation.

R

# import the library
library(caret)

# dataset
data = data.frame(var1 = c(120,345,145,122,596,285,211),
           var2 = c(10,15,45,22,53,28,12),
           var3 = c(-34,0.05,0.15,0.12,-6,0.85,0.11))

# log transform on var2 column of data
logTransformed = log(mydata$var2)
logTransformed

Output:

Log Transformation

Standardization:

Standardization is a technique in which all the features have a mean around zero and have roughly unit variance (mean = 0 and standard deviation = 1). And also makes sure that outliers get weighted more than other values.

Example : Using Standard scale( ) function

Function:

scale(x, center = TRUE, scale = TRUE)

Arguments:

• x – a numeric matrix(like object)
• center – either a logical value or numeric-alike vector of length equal to the number of columns of x
• scale – either a logical value or a numeric-alike vector of length equal to the number of columns of x

scale( ) function (a part of caret package in R) takes in a matrix or dataframe object and scales the data points such that the mean and standard deviation is 0 and 1 respectively.

R

# import the library
library(caret)

# dataset
data = data.frame(var1 = c(120,345,145,122,596,285,211),
           var2 = c(10,15,45,22,53,28,12),
           var3 = c(-34,0.05,0.15,0.12,-6,0.85,0.11))

# standardize the data using scale() function
standardizedData <- as.data.frame(scale(data))
head(standardizedData)

Output:

Example: Using an in-built function in the caret library to preprocess and then standardize the data.

Here the method, preProcess( ) will take a tuple with values “center” and “scale” to implement standardization. This preprocessed data is sent to predict( ) to standardize the data such that the mean is 0 and the standard deviation is 1.

R

# import the library
library(caret)

# dataset
data = data.frame(var1 = c(120,345,145,122,596,285,211),
           var2 = c(10,15,45,22,53,28,12),
           var3 = c(-34,0.05,0.15,0.12,-6,0.85,0.11))

# using caret lib to preprocess data
preproc1 <- preProcess(data, method=c("center", "scale"))

# standardize the preprocessed data
norm1 <- predict(preproc1,data)
head(norm1)

Output: