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)

目录

输出结果

设计思路

核心代码

输出结果

设计思路

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
    
-meta">    @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))
    
-meta">    @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