What is the difference between normalization and standardization?

Normalization and standardization are both techniques used to scale data, but they differ in how they adjust the range and distribution of the values. Here's a breakdown of the two:

1. Normalization

• Definition: Normalization, also called min-max scaling, transforms the data into a specific range, usually [0, 1]. It adjusts the data based on the minimum and maximum values of the feature.
  
• Formula: Xnormalized=X−min⁡(X)max⁡(X)−min⁡(X)X_{ ext{normalized}} = rac{X - min(X)}{max(X) - min(X)}Xnormalized​=max(X)−min(X)X−min(X)​
  
• When to Use: Normalization is useful when the data has different units or scales, especially in algorithms that are sensitive to the magnitude of values, like neural networks or k-nearest neighbors (KNN). It is also ideal when you need features to be within a bounded range.
  

2. Standardization

• Definition: Standardization, also known as Z-score scaling, transforms data to have a mean of 0 and a standard deviation of 1. This is done by subtracting the mean of the feature and dividing by its standard deviation.
  
• Formula: Xstandardized=X−μσX_{ ext{standardized}} = rac{X - mu}{sigma}Xstandardized​=σX−μ​ where μmuμ is the mean and σsigmaσ is the standard deviation of the feature.
  
• When to Use: Standardization is useful when the data is normally distributed or when you’re using algorithms that assume normality, like linear regression, logistic regression, or support vector machines (SVMs). It works well when the data has outliers, as it does not bound the values like normalization.
  

Key Differences

• Range: Normalized data falls within a fixed range (e.g., 0 to 1), while standardized data does not have a fixed range.
  
• Application: Normalization is used when the data needs to be constrained to a specific range, while standardization is better for algorithms that assume a normal distribution.
  

Conclusion

Both techniques are essential for preparing data for machine learning models, and the choice between normalization and standardization depends on the specific algorithm and data characteristics.