Implementation:Scikit learn Scikit learn PolynomialFeatures

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Feature Engineering, Data Preprocessing
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for generating polynomial and interaction features provided by scikit-learn.

Description

PolynomialFeatures generates a new feature matrix consisting of all polynomial combinations of the features with degree less than or equal to the specified degree. For example, if an input sample is two dimensional and of the form [a, b], the degree-2 polynomial features are [1, a, b, a^2, ab, b^2]. This module also includes SplineTransformer for B-spline basis functions.

Usage

Use PolynomialFeatures when you want to add non-linearity to a linear model by generating polynomial and interaction terms from existing features. This is particularly useful for polynomial regression and for capturing feature interactions without manually creating them.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/preprocessing/_polynomial.py

Signature

class PolynomialFeatures(TransformerMixin, BaseEstimator):
    def __init__(
        self, degree=2, *, interaction_only=False, include_bias=True, order="C"
    ):

Import

from sklearn.preprocessing import PolynomialFeatures

I/O Contract

Inputs

Name	Type	Required	Description
degree	int or tuple (min_degree, max_degree)	No	Maximum degree of the polynomial features. Default is 2.
interaction_only	bool	No	If True, only interaction features are produced (no powers of single features). Default is False.
include_bias	bool	No	If True, include a bias column of ones. Default is True.
order	str	No	Order of output array in the dense case. 'F' for Fortran, 'C' for C order. Default is 'C'.

Outputs

Name	Type	Description
X_transformed	ndarray or sparse matrix of shape (n_samples, n_output_features)	The matrix of polynomial features.
n_output_features_	int	The total number of output features after polynomial expansion.
powers_	ndarray of shape (n_output_features, n_features)	The exponent for each of the inputs in the output.

Usage Examples

Basic Usage

from sklearn.preprocessing import PolynomialFeatures
import numpy as np

X = np.array([[1, 2], [3, 4]])
poly = PolynomialFeatures(degree=2, include_bias=False)
X_poly = poly.fit_transform(X)
print(X_poly)
# [[1. 2. 1. 2. 4.]
#  [3. 4. 9. 12. 16.]]
print(poly.get_feature_names_out())
# ['x0', 'x1', 'x0^2', 'x0 x1', 'x1^2']

Related Pages

• Principle:Scikit_learn_Scikit_learn_Feature_Encoding