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In real-world datasets, features often have vastly different scales and units. For example, a dataset might contain house prices (in thousands of dollars), square footage (in hundreds of square feet), and number of bedrooms (single digits). Without standardization, algorithms like LASSO regression or k-means clustering would be dominated by features with larger numeric values, leading to biased results and poor model performance.
Standardization transforms each feature to have a mean of 0 and standard deviation of 1, putting all features on the same scale. This ensures that:
- Regularization penalties treat all features equally
- Distance-based algorithms work correctly
- Gradient-based optimization converges more efficiently
- Model coefficients become comparable across features