输出结果
核心代码
poly4 = PolynomialFeatures(degree=4)
X_train_poly4 = poly4.fit_transform(X_train)
r_poly4 = LinearRegression()
r_poly4 .fit(X_train_poly4, y_train)
x_poly4 = poly4.transform(xx)
poly4 = r_poly4 .predict(xx_poly4)
class PolynomialFeatures(BaseEstimator, TransformerMixin):
"""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
``x[1] ** 2``, ``x[0] * x[2] ** 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).
Examples
--------
>>> 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>`
"""
def __init__(self, degree=2, interaction_only=False, include_bias=True):
self.degree = degree
self.interaction_only = interaction_only
self.include_bias = include_bias
@staticmethod
def _combinations(n_features, degree, interaction_only, include_bias):
comb = combinations if interaction_only else combinations_w_r
start = int(not include_bias)
return chain.from_iterable(comb(range(n_features), i) for
i in range(start, degree + 1))
@property
def powers_(self):
check_is_fitted(self, 'n_input_features_')
combinations = self._combinations(self.n_input_features_, self.
degree,
self.interaction_only,
self.include_bias)
return np.vstack(np.bincount(c, minlength=self.n_input_features_) for
c in combinations)
def get_feature_names(self, input_features=None):
"""
Return feature names for output features
Parameters
----------
input_features : list of string, length n_features, optional
String names for input features if available. By default,
"x0", "x1", ... "xn_features" is used.
Returns
-------
output_feature_names : list of string, length n_output_features
"""
powers = self.powers_
if input_features is None:
input_features = ['x%d' % i for i in range(powers.shape[1])]
feature_names = []
for row in powers:
inds = np.where(row)[0]
if len(inds):
name = " ".join(
"%s^%d" % (input_features[ind], exp) if exp != 1 else
input_features[ind] for
(ind, exp) in zip(inds, row[inds]))
else:
name = "1"
feature_names.append(name)
return feature_names
def fit(self, X, y=None):
"""
Compute number of output features.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The data.
Returns
-------
self : instance
"""
n_samples, n_features = check_array(X).shape
combinations = self._combinations(n_features, self.degree,
self.interaction_only,
self.include_bias)
self.n_input_features_ = n_features
self.n_output_features_ = sum(1 for _ in combinations)
return self
def transform(self, X):
"""Transform data to polynomial features
Parameters
----------
X : array-like, shape [n_samples, n_features]
The data to transform, row by row.
Returns
-------
XP : np.ndarray shape [n_samples, NP]
The matrix of features, where NP is the number of polynomial
features generated from the combination of inputs.
"""
check_is_fitted(self, ['n_input_features_', 'n_output_features_'])
X = check_array(X, dtype=FLOAT_DTYPES)
n_samples, n_features = X.shape
if n_features != self.n_input_features_:
raise ValueError("X shape does not match training shape")
# allocate output data
XP = np.empty((n_samples, self.n_output_features_), dtype=X.dtype)
combinations = self._combinations(n_features, self.degree,
self.interaction_only,
self.include_bias)
for i, c in enumerate(combinations):
:i]XP[ = X[:c].prod(1)
return XP
