What is the mathematical formula for min-max normalization and what range does it produce?

Decision-tree models do not require feature scaling because they split data based on feature conditions (thresholds) rather than absolute magnitudes. Monotonic rescaling of feature values does not change the branching structure or the order of splits.

Conditions: Model is a decision tree or an ensemble of trees (random forest, XGBoost, etc.).; Splitting logic is based on comparing feature values to thresholds.

Feature scaling is needed because raw features often differ in units and magnitudes, making them incomparable. Scaling brings them onto a common scale, which is necessary for many machine learning algorithms to function properly.

Conditions: Dataset contains multiple features with different units or ranges.; The model is sensitive to feature magnitudes (e.g., distance-based or gradient-based).

Import `MinMaxScaler` from `sklearn.preprocessing`, instantiate it, and call `fit_transform` on the selected DataFrame columns. This fits the scaler to the data (learning min/max) and transforms the values to the [0, 1] range.

Conditions: Input data is numerical.; Scikit-learn library is installed.

Standardization transforms a feature value $x$ into $z = \frac{x - \mu}{\sigma}$, targeting a mean of 0 and a standard deviation of 1 for the transformed feature.

Conditions: Applied per numerical feature.; Uses the feature mean $\mu$ and standard deviation $\sigma$.; Assumes $\sigma > 0$.

Import `StandardScaler` from `sklearn.preprocessing`, instantiate it, and call `fit_transform` on the selected DataFrame columns. This transforms the data to have mean 0 and standard deviation 1.

Conditions: Input data is numerical.; Scikit-learn library is installed.