A data scientist is preparing a manufacturing data set for a k-nearest neighbors (k-NN) model that uses Euclidean distance. The data contain two continuous variables: AnnualEnergy_kWh, with a range of 0 to 12,000, and MaintenanceDowntime_min, with a range of 0 to 7,200.
During pilot runs, the distance metric is dominated by AnnualEnergy_kWh, causing records with high downtime to be mis-classified. According to best practice for normalization, which preprocessing step should the data scientist apply before training so that both variables contribute proportionally to the distance calculation?
Apply a natural logarithm transform (log1p) to every value in both features.
Standardize each feature to zero mean and unit variance (z-score).
Generate polynomial cross-terms between the two features and include them in the model.
Rescale each feature to the 0-1 interval using min-max normalization.
The k-nearest neighbors (k-NN) algorithm relies on raw Euclidean distances, so any feature with a larger numeric range will disproportionately dominate the distance metric. Min-max normalization addresses this by rescaling each continuous feature to a common bounded range (typically 0 to 1), ensuring that both AnnualEnergy_kWh and MaintenanceDowntime_min have an equal potential influence on the distance metric. Standardization (z-score) is another common scaling technique, but it scales data based on a mean of 0 and a standard deviation of 1, without enforcing a strict, bounded range; this can make it more sensitive to outliers than min-max normalization. A log transform changes a feature's distribution shape to handle skewness and is not designed for scaling features of different magnitudes. Creating polynomial cross-terms is a feature engineering technique that introduces new, unscaled variables, which would likely worsen the imbalance. Therefore, min-max normalization is the most appropriate technique in this scenario.
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Why is min-max normalization preferred over standardization for k-NN with Euclidean distance?
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