Compare Feature Scaling Methods and Choose the Best for Your Model

Act as a machine learning preprocessing specialist. I am building a [MODEL_TYPE] model (e.g., linear regression, SVM, neural network, random forest) on a dataset with [NUMBER_OF_FEATURES] features. The features include: - [FEATURE_1]: range [MIN_1] to [MAX_1], distribution: [DISTRIBUTION_1] - [FEATURE_2]: range [MIN_2] to [MAX_2], distribution: [DISTRIBUTION_2] - [FEATURE_3]: range [MIN_3] to [MAX_3], distribution: [DISTRIBUTION_3] Please provide a detailed comparison and recommendation: 1. **Method Overview**: Explain the following scaling techniques with mathematical formulas, intuition, and when each is appropriate: - Min-Max Scaling (Normalization) - Standard Scaling (Z-score Standardization) - Robust Scaling (using median and IQR) - MaxAbs Scaling - Power Transformation (Yeo-Johnson / Box-Cox) - Quantile Transformation 2. **Model Compatibility Matrix**: Create a table showing which scaling methods work best with [MODEL_TYPE] and why. Include notes on which models are scale-invariant and which are highly sensitive. 3. **Practical Implementation**: Provide Python code using scikit-learn to apply each method, including proper train/test split handling to avoid data leakage. 4. **Comparison Experiment**: Write a script that trains [MODEL_TYPE] with each scaling method, evaluates using [EVALUATION_METRIC], and outputs a ranked comparison table. 5. **Recommendation**: Based on my feature distributions and model choice, recommend the optimal scaling strategy and explain your reasoning. Highlight common mistakes (e.g., fitting the scaler on the full dataset before splitting) and how to avoid them.