ML之LiR&2PolyR&4PolyR：使用線性回歸LiR、二次多項式回歸2PolyR、四次多項式回歸4PolyR模型在披薩數據集上擬合(train)、價格回歸預測(test)

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目錄

輸出結果

設計思路

核心代碼

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輸出結果

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設計思路

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核心代碼

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 combinationsof 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 : integerThe degree of the polynomial features. Default = 2.interaction_only : boolean, default = FalseIf true, only interaction features are produced: features that areproducts of at most ``degree`` *distinct* input features (so not``x[1] ** 2``, ``x[0] * x[2] ** 3``, etc.).include_bias : booleanIf True (default), then include a bias column, the feature in whichall polynomial powers are zero (i.e. a column of ones - acts as anintercept term in a linear model).Examples-------->>> X = np.arange(6).reshape(3, 2)>>> Xarray([[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_ : intThe total number of input features.n_output_features_ : intThe total number of polynomial output features. The number of outputfeatures is computed by iterating over all suitably sized combinationsof input features.Notes-----Be aware that the number of features in the output array scalespolynomially in the number of features of the input array, andexponentially 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 = degreeself.interaction_only = interaction_onlyself.include_bias = include_bias@staticmethoddef _combinations(n_features, degree, interaction_only, include_bias):comb = combinations if interaction_only else combinations_w_rstart = int(not include_bias)return chain.from_iterable(comb(range(n_features), i) for i in range(start, degree + 1))@propertydef 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 featuresParameters----------input_features : list of string, length n_features, optionalString 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_namesdef 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).shapecombinations = self._combinations(n_features, self.degree, self.interaction_only, self.include_bias)self.n_input_features_ = n_featuresself.n_output_features_ = sum(1 for _ in combinations)return selfdef transform(self, X):"""Transform data to polynomial featuresParameters----------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 polynomialfeatures 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.shapeif n_features != self.n_input_features_:raise ValueError("X shape does not match training shape")# allocate output dataXP = 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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