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feature scaling is an essential step in the data preprocessing phase of machine learning and data analysis, especially when working with algorithms that are sensitive to the scale of the data, such as gradient descent-based algorithms and distance-based algorithms (e.g., k-nearest neighbors, support vector machines). two common methods of feature scaling are *standardization* and **normalization**.

standardization

*standardization* (also known as z-score normalization) transforms the features to have a mean of 0 and a standard deviation of 1. it is done using the following formula:

\[ z = \frac{(x - \mu)}{\sigma} \]

where:
\( z \) is the standardized value,
\( x \) is the original value,
\( \mu \) is the mean of the feature,
\( \sigma \) is the standard deviation of the feature.

when to use standardization:
when the data follows a gaussian distribution (normal distribution).
when you want to center the data around zero.

normalization

*normalization* (also known as min-max scaling) rescales the features to a fixed range, usually [0, 1]. the formula for normalization is:

\[ x' = \frac{(x - x_{min})}{(x_{max} - x_{min})} \]

where:
\( x' \) is the normalized value,
\( x \) is the original value,
\( x_{min} \) is the minimum value of the feature,
\( x_{max} \) is the maximum value of the feature.

when to use normalization:
when the data does not follow a gaussian distribution.
when you want to bound the feature values within a specific range.

code example

let's illustrate both standardization and normalization with a simple code example using python and the popular library `scikit-learn`.



explanation of the code

1. **data creation**: we create a simple dataset with two features, `feature1` and `feature2`.
2. **standardization**:
we instantiate `standardscaler` from `sklearn.preprocessing`.
we fit and transform the data using `fit_transform()`, which scales the data and returns the standardized values.
3. **no ...

#Standardization #Normalization #python
Standardization normalization feature scaling data preprocessing machine learning statistics z-score min-max scaling data transformation standard deviation mean range outliers dataset comparison algorithms