ML之LiR&2PolyR:使用线性回归LiR、二次多项式回归2PolyR模型在披萨数据集上拟合(train)、价格回归预测(test)

输出结果

ML之LiR&2PolyR:使用线性回归LiR、二次多项式回归2PolyR模型在披萨数据集上拟合(train)、价格回归预测(test)

ML之LiR&2PolyR:使用线性回归LiR、二次多项式回归2PolyR模型在披萨数据集上拟合(train)、价格回归预测(test)


设计思路

ML之LiR&2PolyR:使用线性回归LiR、二次多项式回归2PolyR模型在披萨数据集上拟合(train)、价格回归预测(test)


核心代码

poly2 = PolynomialFeatures(degree=2)

X_train_poly2 = poly2.fit_transform(X_train)

r_poly2 = LinearRegression()          

r_poly2.fit(X_train_poly2, y_train)  

poly2 = r_poly2.predict(xx_poly2)


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


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