scikit-learn机器学习(三)多项式回归(二阶，三阶，九阶)

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我们仍然使用披萨直径的价格的数据

import matplotlib

matplotlib.rcParams['font.sans-serif']=[u'simHei']

matplotlib.rcParams['axes.unicode_minus']=False

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression

from sklearn.preprocessing import PolynomialFeatures

X_train = [[6],[8],[10],[14],[18]]

y_train = [[7],[9],[13],[17.5],[18]]

X_test = [[6],[8],[11],[16]]

y_test = [[8],[12],[15],[18]]

LR = LinearRegression()

LR.fit(X_train,y_train)

xx = np.linspace(0,26,100)

yy = LR.predict(xx.reshape(xx.shape[0],1))

plt.plot(xx,yy)

二阶多项式回归

# In[1] 二次回归，二阶多项式回归

#PolynomialFeatures转换器可以用于为一个特征表示增加多项式特征

quadratic_featurizer = PolynomialFeatures(degree=2)

X_train_quadratic = quadratic_featurizer.fit_transform(X_train)

X_test_quadratic = quadratic_featurizer.transform(X_test)

regressor_quadratic = LinearRegression()

regressor_quadratic.fit(X_train_quadratic,y_train)

xx_quadratic = quadratic_featurizer.transform(xx.reshape(xx.shape[0],1))

yy_quadratic = regressor_quadratic.predict(xx_quadratic)

plt.plot(xx,yy_quadratic,c='r',linestyle='--')

# In[2] 图参数，输出结果

plt.title("披萨价格和直径的关系")

plt.xlabel("直径")

plt.ylabel("价格")

plt.axis([0,25,0,25])

plt.grid(True)

plt.scatter(X_train,y_train)

print("X_train\n",X_train)

print("X_train_quadratic\n",X_train_quadratic)

print("X_test\n",X_test)

print("X_test_quadratic\n",X_test_quadratic)

print("简单线性规划R方",LR.score(X_test,y_test))

print("二阶多项式回归R方",regressor_quadratic.score(X_test_quadratic,y_test))

X_train

 [[6], [8], [10], [14], [18]]

X_train_quadratic

 [[  1.   6.  36.]

 [  1.   8.  64.]

 [  1.  10. 100.]

 [  1.  14. 196.]

 [  1.  18. 324.]]

X_test

 [[6], [8], [11], [16]]

X_test_quadratic

 [[  1.   6.  36.]

 [  1.   8.  64.]

 [  1.  11. 121.]

 [  1.  16. 256.]]

简单线性规划R方 0.809726797707665

三阶多项式回归

# In[3] 尝试三阶多项式回归

cubic_featurizer = PolynomialFeatures(degree=3)

X_train_cubic = cubic_featurizer.fit_transform(X_train)

X_test_cubic = cubic_featurizer.transform(X_test)

regressor_cubic = LinearRegression()

regressor_cubic.fit(X_train_cubic,y_train)

xx_cubic = cubic_featurizer.transform(xx.reshape(xx.shape[0],1))

yy_cubic = regressor_cubic.predict(xx_cubic)

plt.plot(xx,yy_cubic,c='g',linestyle='--')

plt.show()

print("X_train\n",X_train)

print("X_train_cubic\n",X_train_cubic)

print("X_test\n",X_test)

print("X_test_cubic\n",X_test_cubic)

print("三阶多项式回归R方",regressor_cubic.score(X_test_cubic,y_test))

X_train

 [[6], [8], [10], [14], [18]]

X_train_cubic

 [[1.000e+00 6.000e+00 3.600e+01 2.160e+02]

 [1.000e+00 8.000e+00 6.400e+01 5.120e+02]

 [1.000e+00 1.000e+01 1.000e+02 1.000e+03]

 [1.000e+00 1.400e+01 1.960e+02 2.744e+03]

 [1.000e+00 1.800e+01 3.240e+02 5.832e+03]]

X_test

 [[6], [8], [11], [16]]

X_test_cubic

 [[1.000e+00 6.000e+00 3.600e+01 2.160e+02]

 [1.000e+00 8.000e+00 6.400e+01 5.120e+02]

 [1.000e+00 1.100e+01 1.210e+02 1.331e+03]

 [1.000e+00 1.600e+01 2.560e+02 4.096e+03]]

三阶多项式回归R方 0.8356924156036954

九阶多项式回归

# In[4] 尝试九阶多项式回归

nine_featurizer = PolynomialFeatures(degree=9)

X_train_nine = nine_featurizer.fit_transform(X_train)

X_test_nine = nine_featurizer.transform(X_test)

regressor_nine = LinearRegression()

regressor_nine.fit(X_train_nine,y_train)

xx_nine = nine_featurizer.transform(xx.reshape(xx.shape[0],1))

yy_nine = regressor_nine.predict(xx_nine)

plt.plot(xx,yy_nine,c='k',linestyle='--')

plt.show()

print("X_train\n",X_train)

print("X_train_nine\n",X_train_nine)

print("X_test\n",X_test)

print("X_test_nine\n",X_test_nine)

print("九阶多项式回归R方",regressor_nine.score(X_test_nine,y_test))

X_train

 [[6], [8], [10], [14], [18]]

X_train_nine

 [[1.00000000e+00 6.00000000e+00 3.60000000e+01 2.16000000e+02

  1.29600000e+03 7.77600000e+03 4.66560000e+04 2.79936000e+05

  1.67961600e+06 1.00776960e+07]

 [1.00000000e+00 8.00000000e+00 6.40000000e+01 5.12000000e+02

  4.09600000e+03 3.27680000e+04 2.62144000e+05 2.09715200e+06

  1.67772160e+07 1.34217728e+08]

 [1.00000000e+00 1.00000000e+01 1.00000000e+02 1.00000000e+03

  1.00000000e+04 1.00000000e+05 1.00000000e+06 1.00000000e+07

  1.00000000e+08 1.00000000e+09]

 [1.00000000e+00 1.40000000e+01 1.96000000e+02 2.74400000e+03

  3.84160000e+04 5.37824000e+05 7.52953600e+06 1.05413504e+08

  1.47578906e+09 2.06610468e+10]

 [1.00000000e+00 1.80000000e+01 3.24000000e+02 5.83200000e+03

  1.04976000e+05 1.88956800e+06 3.40122240e+07 6.12220032e+08

  1.10199606e+10 1.98359290e+11]]

X_test

 [[6], [8], [11], [16]]

X_test_nine

 [[1.00000000e+00 6.00000000e+00 3.60000000e+01 2.16000000e+02

  1.29600000e+03 7.77600000e+03 4.66560000e+04 2.79936000e+05

  1.67961600e+06 1.00776960e+07]

 [1.00000000e+00 8.00000000e+00 6.40000000e+01 5.12000000e+02

  4.09600000e+03 3.27680000e+04 2.62144000e+05 2.09715200e+06

  1.67772160e+07 1.34217728e+08]

 [1.00000000e+00 1.10000000e+01 1.21000000e+02 1.33100000e+03

  1.46410000e+04 1.61051000e+05 1.77156100e+06 1.94871710e+07

  2.14358881e+08 2.35794769e+09]

 [1.00000000e+00 1.60000000e+01 2.56000000e+02 4.09600000e+03

  6.55360000e+04 1.04857600e+06 1.67772160e+07 2.68435456e+08

  4.29496730e+09 6.87194767e+10]]

九阶多项式回归R方 -0.09435666704291412

所有代码

# -*- coding: utf-8 -*-

import matplotlib

matplotlib.rcParams['font.sans-serif']=[u'simHei']

matplotlib.rcParams['axes.unicode_minus']=False

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression

from sklearn.preprocessing import PolynomialFeatures

X_train = [[6],[8],[10],[14],[18]]

y_train = [[7],[9],[13],[17.5],[18]]

X_test = [[6],[8],[11],[16]]

y_test = [[8],[12],[15],[18]]

LR = LinearRegression()

LR.fit(X_train,y_train)

xx = np.linspace(0,26,100)

yy = LR.predict(xx.reshape(xx.shape[0],1))

plt.plot(xx,yy)

# In[1] 二次回归，二阶多项式回归

#PolynomialFeatures转换器可以用于为一个特征表示增加多项式特征

quadratic_featurizer = PolynomialFeatures(degree=2)

X_train_quadratic = quadratic_featurizer.fit_transform(X_train)

X_test_quadratic = quadratic_featurizer.transform(X_test)

regressor_quadratic = LinearRegression()

regressor_quadratic.fit(X_train_quadratic,y_train)

xx_quadratic = quadratic_featurizer.transform(xx.reshape(xx.shape[0],1))

yy_quadratic = regressor_quadratic.predict(xx_quadratic)

plt.plot(xx,yy_quadratic,c='r',linestyle='--')

# In[2] 图参数，输出结果

plt.title("披萨价格和直径的关系")

plt.xlabel("直径")

plt.ylabel("价格")

plt.axis([0,25,0,25])

plt.grid(True)

plt.scatter(X_train,y_train)

print("X_train\n",X_train)

print("X_train_quadratic\n",X_train_quadratic)

print("X_test\n",X_test)

print("X_test_quadratic\n",X_test_quadratic)

print("简单线性规划R方",LR.score(X_test,y_test))

print("二阶多项式回归R方",regressor_quadratic.score(X_test_quadratic,y_test))

# In[3] 尝试三阶多项式回归

cubic_featurizer = PolynomialFeatures(degree=3)

X_train_cubic = cubic_featurizer.fit_transform(X_train)

X_test_cubic = cubic_featurizer.transform(X_test)

regressor_cubic = LinearRegression()

regressor_cubic.fit(X_train_cubic,y_train)

xx_cubic = cubic_featurizer.transform(xx.reshape(xx.shape[0],1))

yy_cubic = regressor_cubic.predict(xx_cubic)

plt.plot(xx,yy_cubic,c='g',linestyle='--')

plt.show()

print("X_train\n",X_train)

print("X_train_cubic\n",X_train_cubic)

print("X_test\n",X_test)

print("X_test_cubic\n",X_test_cubic)

print("三阶多项式回归R方",regressor_cubic.score(X_test_cubic,y_test))

# In[4] 尝试九阶多项式回归

nine_featurizer = PolynomialFeatures(degree=9)

X_train_nine = nine_featurizer.fit_transform(X_train)

X_test_nine = nine_featurizer.transform(X_test)

regressor_nine = LinearRegression()

regressor_nine.fit(X_train_nine,y_train)

xx_nine = nine_featurizer.transform(xx.reshape(xx.shape[0],1))

yy_nine = regressor_nine.predict(xx_nine)

plt.plot(xx,yy_nine,c='k',linestyle='--')

plt.show()

print("X_train\n",X_train)

print("X_train_nine\n",X_train_nine)

print("X_test\n",X_test)

print("X_test_nine\n",X_test_nine)

print("九阶多项式回归R方",regressor_nine.score(X_test_nine,y_test))