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
.
Parameters ---------- degree : integer The degree of the polynomial features. Default = 2.
interaction_only : boolean, default = False If true, only interaction features are produced: features that are products of at most ``degree`` *distinct* input features (so not ``x1
** 2``, ``x0
* x2
** 3``, etc.).
include_bias : boolean 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 : str in 'C', 'F'
, default 'C' Order of output array in the dense case. 'F' order is faster to compute, but may slow down subsequent estimators.
.. versionadded:: 0.21
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.]
)
Attributes ---------- powers_ : array, shape (n_output_features, n_input_features) powers_i, j
is the exponent of the jth input in the ith output.
n_input_features_ : int The total number of input features.
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.
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 :ref:`examples/linear_model/plot_polynomial_interpolation.py <sphx_glr_auto_examples_linear_model_plot_polynomial_interpolation.py>`