Data Science – How to Scale or Normalize Numeric Data using R

This article represents concepts around need to normalize or scale the numeric data and code samples in R programming language which could be used to normalize or scale the data. Please feel free to comment/suggest if I missed to mention one or more important points. Also, sorry for the typos.
Following are the two different ways which could be used to nromalize the data, and thus, described later in this article:

  • Why Normalize or Scale the data?
  • Min-Max Normalization
  • Z-Score Standardization


Why Normalize or Scale the data?

There can be instances found in data frame where values for one feature could range between 1-100 and values for other feature could range from 1-10000000. In scenarios like these, owing to mere greater numeric range, the impact on response variables by the feature having greater numeric range could be more than the one having less numeric range, and this could, in turn, impact prediction accuracy. The objective is to improve predictive accuracy and not allow a particular feature impact the prediction due to large numeric value range. Thus, we may need to normalize or scale values under different features such that they fall under common range. Take a look at following example:

# Age vector
age <- c(25, 35, 50)
# Salary vector
salary <- c(200000, 1200000, 2000000)
# Data frame created using age and salary
df <- data.frame( "Age" = age, "Salary" = salary, stringsAsFactors = FALSE)

Above data frame gets printed as following:

  Age  Salary
1  25  200000
2  35 1200000
3  50 2000000

Pay attention to how values for age and salary varies in different ranges.


Min-Max Normalization

Above data frame could be normalized using Min-Max normalization technique which specify following formula to be applied on each value of features to be normalized. This technique is traditionally used with K-Nearest Neighbors (KNN) Classification problems.

(X - min(X))/(max(X) - min(X))

Above could be programmed as following function in R:

normalize <- function(x) {
    return ((x - min(x)) / (max(x) - min(x)))

In order to apply above normalize function on each of the features of above data frame, df, following code could be used. Pay attention to usage of lapply function.

dfNorm <-, normalize))
# One could also use sequence such as df[1:2]
dfNorm <-[1:2], normalize))

In case, one wish to specify a set of features such as salary, following formula could be used:

# Note df[2]
dfNorm <-[2], normalize))
# Note df["Salary"]
dfNorm <-["Salary"], normalize))


Z-Score Standardization

The disadvantage with min-max normalization technique is that it tends to bring data towards the mean. If there is a need for outliers to get weighted more than the other values, z-score standardization technique suits better. In order to achieve z-score standardization, one could use R’s built-in scale() function. Take a look at following example where scale function is applied on “df” data frame mentioned above.

dfNormZ <- scale(df[1:2] ))

Following gets printed as dfNormZ

         Age      Salary
1 -0.9271726 -1.03490978
2 -0.1324532  0.07392213
3  1.0596259  0.96098765


Ajitesh Kumar

Ajitesh Kumar

Ajitesh is passionate about various different technologies including programming languages such as Java/JEE, Javascript, PHP, .NET, C/C++, mobile programming languages etc and, computing fundamentals such as application security, cloud computing, API, mobile apps, google glass, big data etc.Recently, he has been digging deep into the field of data science and machine learning.

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Ajitesh Kumar

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