RFE is a feature selection technique that aims to identify the most important features (variables) within a dataset for creating a machine learning model. It operates by iteratively removing the least important features and retraining the model until the desired number of features remains.

Key Purposes

1. Improving Model Performance: Removing irrelevant or redundant features can often increase the accuracy and efficiency of machine learning models.
2. Combatting Overfitting: Overfitting occurs when models become overly complex and fit noise in the data. RFE helps reduce model complexity, and in turn, overfitting.
3. Enhance Interpretability: Models with fewer, but highly relevant features, are generally easier to understand and explain.

Strengths

• Versatility: RFE can be used with a wide variety of machine learning algorithms (supervised models that provide feature importance as an output).
• Computational Efficiency: While a wrapper method, RFE is often reasonably efficient, especially with linear models.
• Flexibility: Can be customized by the choice of machine learning algorithm and method for ranking feature importance.

Weaknesses

• Greedy Optimization: RFE might overlook the potential importance of combinatorial effects when some features only provide predictive power in combination with others.
• Sensitivity to the Base Model: The optimal subset of features may depend on the choice of the core machine learning algorithm used within RFE.
• Not Directly an Embedded Method: RFE is a wrapper technique, meaning it is an outer loop around a chosen model. Some embedded methods can provide feature selection implicitly as part of the model's construction.

How RFE Works

1. Choose an Estimator: Select a supervised machine learning algorithm which has the capability of ranking features by their importance (e.g., linear models with coefficients, decision trees, random forests).
2. Initial Fit: Train the chosen model on all features in your dataset.
3. Feature Ranking: Determine the importance of each feature. This is usually based on feature coefficients (for linear models) or feature importance scores (for tree-based methods).
4. Elimination: Remove the least important feature(s) based on the ranking.
5. Retrain and Repeat: Fit the model on the pruned feature set and repeat steps 3-4 until the desired number of features remains.
6. Final Feature Set: The features in the final iteration with the best model performance serve as the selected subset.