Cannot understand with sklearn’s PolynomialFeatures

Introduction to PolynomialFeatures in sklearn

In the realm of machine learning, feature engineering plays a crucial role in transforming raw data into a form suitable for model training. One powerful technique for enhancing the predictive power of models is polynomial feature generation, and sklearn’s PolynomialFeatures class provides a convenient way to achieve this.

What are Polynomial Features?

Polynomial features are created by raising existing features to various powers. For instance, if you have a feature ‘x’, creating polynomial features up to degree 2 would involve adding terms like ‘x^2’ and ‘x’ to the dataset. This process effectively introduces non-linear relationships into your data, allowing models to capture more complex patterns.

Understanding sklearn’s PolynomialFeatures

Basic Usage

Here’s how to use PolynomialFeatures to generate polynomial features:

from sklearn.preprocessing import PolynomialFeatures
import numpy as np

# Create an array of features
X = np.array([[1, 2], [3, 4]])

# Instantiate PolynomialFeatures with degree 2
poly = PolynomialFeatures(degree=2)

# Generate polynomial features
poly_features = poly.fit_transform(X)

# Print the transformed data
print(poly_features)

[[1. 1. 2. 1. 2. 4.]
 [1. 3. 4. 9. 12. 16.]]

In this example, we created polynomial features up to degree 2. The output shows the original features along with the new features: ‘x^2’, ‘x*y’, and ‘y^2’.

Understanding the Output

The output of fit_transform is a new array where each row represents a sample, and each column represents a feature. The columns are arranged as follows:

• Constant term (always 1)
• Original features
• Polynomial features (in lexicographic order)

Controlling Feature Generation

You can customize the feature generation using these parameters:

Example with Interaction-Only Features

# Generate only interaction features
poly = PolynomialFeatures(degree=2, interaction_only=True, include_bias=False)
poly_features = poly.fit_transform(X)
print(poly_features)

[[1. 2. 4.]
 [3. 4. 12.]]

Applications of PolynomialFeatures

Polynomial features are commonly used in:

• Nonlinear Regression: Capturing non-linear relationships between features and target variables.
• Feature Engineering for Classifiers: Enhancing the expressiveness of features for better classification performance.
• Dimensionality Reduction: Identifying key interactions between features.

Conclusion

Sklearn’s PolynomialFeatures is a valuable tool for enriching your feature space by introducing non-linear relationships. By understanding its usage and customization options, you can effectively leverage polynomial features to improve the performance of your machine learning models.