Toggle Menu
Prev Up Next

scikit-learn 1.3.2
Other versions

Please cite us if you use the software.

# `sklearn.preprocessing`.PolynomialFeatures

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

  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].

  Read more in the User Guide.

  Parameters:
    degree int or tuple (min_degree, max_degree), default=2

      If a single int is given, it specifies the maximal degree of the polynomial features. If a tuple `(min_degree, max_degree)` is passed, then `min_degree` is the minimum and `max_degree` is the maximum polynomial degree of the generated features. Note that `min_degree=0` and `min_degree=1` are equivalent as outputting the degree zero term is determined by `include_bias`.

    interaction_only bool, default=False

      If `True`, only interaction features are produced: features that are products of at most `degree` distinct input features, i.e. terms with power of 2 or higher of the same input feature are excluded:

      > - included: `x[0]`, `x[1]`, `x[0] * x[1]`, etc.

      > - excluded: `x[0] ** 2`, `x[0] ** 2 * x[1]`, etc.

    include_bias bool, default=True

      If `True` (default), then include a bias column, the feature in which all polynomial powers are zero (i.e. a column of ones - acts as an intercept term in a linear model).

    order{‘C’, ‘F’}, default=’C’

      Order of output array in the dense case. `'F'` order is faster to compute, but may slow down subsequent estimators.

      New in version 0.21.

  Attributes:
    `powers_`ndarray of shape (`n_output_features_`, `n_features_in_`)

      Exponent for each of the inputs in the output.

    n_features_in_int

      Number of features seen during fit.

      New in version 0.24.

    feature_names_in_ndarray of shape (`n_features_in_`,)

      Names of features seen during fit. Defined only when `X` has feature names that are all strings.

      New in version 1.0.

    n_output_features_int

      The total number of polynomial output features. The number of output features is computed by iterating over all suitably sized combinations of input features.

  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_out`([input_features]) | Get output feature names for transformation.
  `get_metadata_routing`() | Get metadata routing of this object.
  `get_params`([deep]) | Get parameters for this estimator.
  `set_output`(*[, transform]) | Set output container.
  `set_params`(**params) | Set the parameters of this estimator.
  `transform`(X) | Transform data to polynomial features.

  fit(X, y=None)

    Compute number of output features.

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

        The data.

      y Ignored

        Not used, present here for API consistency by convention.

    Returns:
      self object

        Fitted transformer.

  fit_transform(X, y=None, **fit_params)

    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:
      X array-like of shape (n_samples, n_features)

        Input samples.

      y array-like of shape (n_samples,) or (n_samples, n_outputs), default=None

        Target values (None for unsupervised transformations).

      **fit_params dict

        Additional fit parameters.

    Returns:
      X_new ndarray array of shape (n_samples, n_features_new)

        Transformed array.

  get_feature_names_out(input_features=None)

    Get output feature names for transformation.

    Parameters:
      input_features array-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_out ndarray of str objects

        Transformed feature names.

  get_metadata_routing()

    Get metadata routing of this object.

    Please check User Guide on how the routing mechanism works.

    Returns:
      routing MetadataRequest

        A `MetadataRequest` encapsulating routing information.

  get_params(deep=True)

    Get parameters for this estimator.

    Parameters:
      deep bool, default=True

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

    Returns:
      params dict

        Parameter names mapped to their values.

  property powers_

    Exponent for each of the inputs in the output.

  set_output(*, transform=None)

    Set output container.

    See Introducing the set_output API for an example on how to use the API.

    Parameters:
      transform{“default”, “pandas”}, default=None

        Configure output of `transform` and `fit_transform`.

        - `"default"`: Default output format of a transformer

        - `"pandas"`: DataFrame output

        - `None`: Transform configuration is unchanged

    Returns:
      self estimator instance

        Estimator instance.

  set_params(**params)

    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:
      **params dict

        Estimator parameters.

    Returns:
      self estimator instance

        Estimator instance.

  transform(X)

    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`.

## Examples using `sklearn.preprocessing.PolynomialFeatures`

Release Highlights for scikit-learn 0.24

Release Highlights for scikit-learn 0.24

Time-related feature engineering

Time-related feature engineering

Comparing Linear Bayesian Regressors

Comparing Linear Bayesian Regressors

Poisson regression and non-normal loss

Poisson regression and non-normal loss

Polynomial and Spline interpolation

Polynomial and Spline interpolation

Robust linear estimator fitting

Robust linear estimator fitting

Displaying Pipelines

Displaying Pipelines

Underfitting vs. Overfitting

Underfitting vs. Overfitting

Plot classification boundaries with different SVM Kernels

Plot classification boundaries with different SVM Kernels