What is Feature Scaling?

Feature scaling is a method used to normalize the range of independent variables or features of data. In data processing, it is also known as data normalization and is generally performed during the data preprocessing step. Just to give you an example — if you have multiple independent variables like age, salary, and height; With their range as (18–100 Years), (25,000–75,000 Euros), and (1–2 Meters) respectively, feature scaling would help them all to be in the same range, for example- centered around 0 or in the range (0,1) depending on the scaling technique.

Methods for Scaling

Normalization and Standardization

Normalization

Also known as min-max scaling or min-max normalization, it is the simplest method and consists of rescaling the range of features to scale the range in [0, 1]. The general formula for normalization is given as:

Here, max(x) and Min(x) are the maximum and the minimum values of the feature respectively.

We can also do a normalization over different intervals, e.g. choosing to have the variable laying in any [a, b] interval, a and b being real numbers. To rescale a range between an arbitrary set of values [a, b], the formula becomes:

Standardization

Feature standardization makes the values of each feature in the data have zero mean and unit variance. The general method of calculation is to determine the distribution mean and standard deviation for each feature and calculate the new data point by the following formula:

Here, σ is the standard deviation of the feature vector, and x? is the average of the feature vector.