scikit-learn机器学习(三)多项式回归(二阶，三阶，九阶)

不念不忘少年蓝@ 2021-11-29 08:56 358阅读 0赞

**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))

![1322499-20190715113258770-1102348561.png][]

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))

![1322499-20190715113511517-175856007.png][]

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))

**![1322499-20190715113737253-154444606.png][]**

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))

![1322499-20190715113908543-243479369.png][]

转载于:https://www.cnblogs.com/caiyishuai/p/11187932.html

[1322499-20190715113258770-1102348561.png]: /images/20211129/4c10ecaac5254d6c912efcdbf7579e7e.png
[1322499-20190715113511517-175856007.png]: /images/20211129/9d32e4e2fb3247a4b6174adede403144.png
[1322499-20190715113737253-154444606.png]: /images/20211129/870d5ef268c64eff8cc17984b1c8d759.png
[1322499-20190715113908543-243479369.png]: /images/20211129/061b43a3b2ae4022b24a8c781e17bd70.png