`sklearn.preprocessing`.PolynomialFeatures¶

class sklearn.preprocessing.PolynomialFeatures(degree=2, *, interaction_only=False, include_bias=True, order='C')[source]¶

Generate polynomial and interaction features.

Generate 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].

See also

SplineTransformer: Transformer that generates univariate B-spline bases for features.

Notes

Be aware that the number of features in the output array scales polynomially in the number of features of the input array, and exponentially in the degree. High degrees can cause overfitting.

See examples/linear_model/plot_polynomial_interpolation.py

Examples

>>> import numpy as np
>>> from sklearn.preprocessing import PolynomialFeatures
>>> X = np.arange(6).reshape(3, 2)
>>> X
array([[0, 1],
       [2, 3],
       [4, 5]])
>>> poly = PolynomialFeatures(2)
>>> poly.fit_transform(X)
array([[ 1.,  0.,  1.,  0.,  0.,  1.],
       [ 1.,  2.,  3.,  4.,  6.,  9.],
       [ 1.,  4.,  5., 16., 20., 25.]])
>>> poly = PolynomialFeatures(interaction_only=True)
>>> poly.fit_transform(X)
array([[ 1.,  0.,  1.,  0.],
       [ 1.,  2.,  3.,  6.],
       [ 1.,  4.,  5., 20.]])

Methods

`fit`(X[, y])	Compute number of output features.
`fit_transform`(X[, y])	Fit to data, then transform it.
`get_feature_names`([input_features])	DEPRECATED: get_feature_names is deprecated in 1.0 and will be removed in 1.2.
`get_feature_names_out`([input_features])	Get output feature names for transformation.
`get_params`([deep])	Get parameters for this estimator.
`set_params`(**params)	Set the parameters of this estimator.
`transform`(X)	Transform data to polynomial features.

fit(X, y=None)[source]¶

Compute number of output features.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features): The data.
yIgnored: Not used, present here for API consistency by convention.

Returns:

selfobject: Fitted transformer.

fit_transform(X, y=None, **fit_params)[source]¶

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters:

Xarray-like of shape (n_samples, n_features): Input samples.
yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None: Target values (None for unsupervised transformations).
**fit_paramsdict: Additional fit parameters.

Returns:

X_newndarray array of shape (n_samples, n_features_new): Transformed array.

get_feature_names(input_features=None)[source]¶

DEPRECATED: get_feature_names is deprecated in 1.0 and will be removed in 1.2. Please use get_feature_names_out instead.

Return feature names for output features.

Parameters:

input_featureslist of str of shape (n_features,), default=None: String names for input features if available. By default, “x0”, “x1”, … “xn_features” is used.

Returns:

output_feature_nameslist of str of shape (n_output_features,): Transformed feature names.

get_feature_names_out(input_features=None)[source]¶

Get output feature names for transformation.

Parameters:

input_featuresarray-like of str or None, default=None

Input features.

If input_features is None, then feature_names_in_ is used as feature names in. If feature_names_in_ is not defined, then the following input feature names are generated: ["x0", "x1", ..., "x(n_features_in_ - 1)"].
If input_features is an array-like, then input_features must match feature_names_in_ if feature_names_in_ is defined.

Returns:

feature_names_outndarray of str objects: Transformed feature names.

get_params(deep=True)[source]¶

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

property n_input_features_¶: DEPRECATED: The attribute n_input_features_ was deprecated in version 1.0 and will be removed in 1.2.

property powers_¶: Exponent for each of the inputs in the output.

set_params(**params)[source]¶

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

transform(X)[source]¶

Transform data to polynomial features.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features)

The data to transform, row by row.

Prefer CSR over CSC for sparse input (for speed), but CSC is required if the degree is 4 or higher. If the degree is less than 4 and the input format is CSC, it will be converted to CSR, have its polynomial features generated, then converted back to CSC.

If the degree is 2 or 3, the method described in “Leveraging Sparsity to Speed Up Polynomial Feature Expansions of CSR Matrices Using K-Simplex Numbers” by Andrew Nystrom and John Hughes is used, which is much faster than the method used on CSC input. For this reason, a CSC input will be converted to CSR, and the output will be converted back to CSC prior to being returned, hence the preference of CSR.

Returns:

XP{ndarray, sparse matrix} of shape (n_samples, NP): The matrix of features, where NP is the number of polynomial features generated from the combination of inputs. If a sparse matrix is provided, it will be converted into a sparse csr_matrix.