Create a Feature Scaling Comparison Plan for Machine Learning Datasets

You are a data science expert specializing in feature engineering and preprocessing. I need a comprehensive feature scaling comparison analysis for my dataset. **Dataset Context:** - Dataset name/domain: [DATASET_NAME] - Number of features: [NUM_FEATURES] - Feature types: [FEATURE_TYPES e.g., continuous, skewed, mixed] - Target variable: [TARGET_VARIABLE] - ML algorithm(s) planned: [ALGORITHMS e.g., SVM, KNN, Linear Regression, Random Forest] **Please provide the following:** 1. **Scaling Methods Overview:** Compare at least 5 scaling techniques (Min-Max Scaling, Standard Scaling, Robust Scaling, MaxAbs Scaling, and Log/Power Transforms). For each, explain the mathematical formula, when it's most appropriate, and its sensitivity to outliers. 2. **Algorithm-Specific Recommendations:** Based on the ML algorithms I listed, recommend which scaling method pairs best with each algorithm and explain why. Include cases where scaling is unnecessary. 3. **Diagnostic Checklist:** Provide a step-by-step checklist I should follow before choosing a scaler, including distribution analysis, outlier detection, and skewness tests. 4. **Code Template:** Write a Python code template using scikit-learn that applies each scaling method to my dataset, visualizes the before-and-after distributions side by side, and outputs summary statistics for comparison. 5. **Evaluation Strategy:** Describe how to empirically test which scaling method yields the best model performance, including metrics to track and a comparison table format. 6. **Common Pitfalls:** List at least 4 common mistakes practitioners make when scaling features (e.g., data leakage during scaling) and how to avoid them. Format the output with clear headings, bullet points, and code blocks where appropriate.