Why do we need feature scaling when columns have different magnitudes?

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.

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.

Min-max normalization transforms a feature value $X$ into $X_{\text{norm}} = \frac{X - X_{\min}}{X_{\max} - X_{\min}}$, mapping the feature's observed range onto the interval $[0, 1]$.

Conditions: Applied per numerical feature.; Requires a finite minimum $X_{\min}$ and maximum $X_{\max}$ for the feature.; Assumes $X_{\max} \neq X_{min}$ to avoid division by zero.