Normalization

Normalization is a technique often applied as part of data preparation for machine learning. The goal of normalization is to change the values of numeric columns in the dataset to a common scale, without distorting differences in the ranges of values or losing information.

Min-Max Normalization

Min-Max normalization is one of the most common ways to normalize data. For every feature, the minimum value of that feature gets transformed into a 0, the maximum value gets transformed into a 1, and every other value gets transformed into a decimal between 0 and 1.

Process:

copy





x_normalized = (x−min(x))/ (max(x)-min(x))

Where:

• x_normalized is the normalized value of the feature.
• x is the original value of the feature.
• min(x) is the minimum value of the feature across the dataset.
• max(x) is the maximum value of the feature across the dataset.

Example:

Unit Normalization

Unit normalization consists of dividing every entry in a column (feature) by its magnitude to create a feature of length 1 known as the unit vector.

Process:

copy





x_normalized =  x / ||x||

Where:

• x_normalized is the normalized value of the feature.
• x is the original value of the feature.
• ||x|| is the magnitude which is calculated as
• ||x|| = sqrt(x1^2 + x2^2 + ……. xn^2)
• x1, x2, x3……xn are the original values of the feature.

Example:

Mean Normalization

This transformer transforms the data based on the mean so that sum of the values equals to 0.

Process:

copy





x_normalized =  x - mean(x) /  max(x) - min(x)

Where:

• x_normalized is the normalized value of the feature.
• x is the original value of the feature.
• mean(x) is the mean of feature across the dataset.
• min(x) is the minimum value of the feature across the dataset.
• max(x) is the maximum value of the feature across the dataset.

Example:

Mean-Std Normalization

The data can be normalized by subtracting the mean (µ) of each feature and a division by the standard deviation (σ). This way, each feature has a mean of 0 and a standard deviation of 1. This results in faster convergence.

Process:

copy





x_normalized =  x - mean(x) /  std(x)

Where

• x_normalized is the normalized value of the feature.
• x is the original value of the feature.
• mean(x) is the mean of feature across the dataset.
• std(x) is the standard deviation of the feature across the dataset.

Example: