What normalization methods for data distribution exist?

Data distribution normalization is an important preprocessing step in machine learning that helps improve model quality. Main normalization methods:

• Min-Max Normalization: transforms data into a specified range, usually [0,1].

  Formula: ( x' = \frac{x - x_{min}}{x_{max} - x_{min}} )

• Z-normalization (Standardization): brings data to a distribution with zero mean and unit variance.

  Formula: ( x' = \frac{x - \mu}{\sigma} ), where (\mu) is the mean, (\sigma) is the standard deviation.

• Robust Scaling: uses median and interquartile range, resistant to outliers.

• Logarithmic Transformation: used to shift the distribution closer to normal.

• Box-Cox and Yeo-Johnson transformations: more complex methods for normalization, especially when data is heavily skewed.

The choice of method depends on the nature of the data and model requirements. For example, algorithms sensitive to scale (SVM, KNN) often use standardization or min-max normalization.