sklearn逻辑回归实战

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题目要求

根据学生两门课的成绩和是否入学的数据，预测学生能否顺利入学：利用ex2data1.txt和ex2data2.txt中的数据，进行逻辑回归和预测。

数据放在最后边。

ex2data1.txt处理

作散点图可知，决策大致符合线性关系，但还是有弯曲（非线性），用线性效果并不好，因此可用两种方案：方案一，无多项式特征；方案二，有多项式特征。

方案一：无多项式特征

对ex2data1.txt中的数据进行逻辑回归，无多项式特征

代码实现如下：

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"""
    对ex2data1.txt中的数据进行逻辑回归（无多项式特征）
"""
from sklearn.model_selection import train_test_split
from matplotlib.colors import ListedColormap
from sklearn.linear_model import LogisticRegression
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号

# 数据格式：成绩1,成绩2,是否被录取（1代表被录取，0代表未被录取）


# 函数（画决策边界）定义
def plot_decision_boundary(model, axis):
    x0, x1 = np.meshgrid(
        np.linspace(axis[0], axis[1], int((axis[1] - axis[0]) * 100)).reshape(-1, 1),
        np.linspace(axis[2], axis[3], int((axis[3] - axis[2]) * 100)).reshape(-1, 1),
    )
    X_new = np.c_[x0.ravel(), x1.ravel()]

    y_predict = model.predict(X_new)
    zz = y_predict.reshape(x0.shape)

    custom_cmap = ListedColormap(['#EF9A9A', '#FFF59D', '#90CAF9'])

    plt.contourf(x0, x1, zz, cmap=custom_cmap)

# 读取数据
data = np.loadtxt('ex2data1.txt', delimiter=',')
data_X = data[:, 0:2]
data_y = data[:, 2]

# 数据分割
X_train, X_test, y_train, y_test = train_test_split(data_X, data_y, random_state=666)

# 训练模型
log_reg = LogisticRegression()
log_reg.fit(X_train, y_train)

# 结果可视化
plot_decision_boundary(log_reg, axis=[0, 100, 0, 100])
plt.scatter(data_X[data_y == 0, 0], data_X[data_y == 0, 1], color='red')
plt.scatter(data_X[data_y == 1, 0], data_X[data_y == 1, 1], color='blue')
plt.xlabel('成绩1')
plt.ylabel('成绩2')
plt.title('两门课程成绩与是否录取的关系')
plt.show()

# 模型测试
print(log_reg.score(X_train, y_train))
print(log_reg.score(X_test, y_test))

输出结果如下：

1
2
0.8533333333333334
0.76

ex2data1逻辑回归（无多项式）.png

方案二：引入多项式特征

对ex2data1.txt中的数据进行逻辑回归，引入多项式特征。经调试，当degree为3时，耗费时间较长；当degree为2时，耗费时间可接受，效果与方案一相比好了很多

实现如下：

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"""
    对ex2data1.txt中的数据进行逻辑回归（引入多项式特征）
"""
from sklearn.model_selection import train_test_split
from matplotlib.colors import ListedColormap
from sklearn.linear_model import LogisticRegression
import numpy as np
import matplotlib.pyplot as plt
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号

# 数据格式：成绩1,成绩2,是否被录取（1代表被录取，0代表未被录取）


# 函数定义
def plot_decision_boundary(model, axis):
    x0, x1 = np.meshgrid(
        np.linspace(axis[0], axis[1], int((axis[1] - axis[0]) * 100)).reshape(-1, 1),
        np.linspace(axis[2], axis[3], int((axis[3] - axis[2]) * 100)).reshape(-1, 1),
    )
    X_new = np.c_[x0.ravel(), x1.ravel()]

    y_predict = model.predict(X_new)
    zz = y_predict.reshape(x0.shape)

    custom_cmap = ListedColormap(['#EF9A9A', '#FFF59D', '#90CAF9'])

    plt.contourf(x0, x1, zz, cmap=custom_cmap)


def PolynomialLogisticRegression(degree):
    return Pipeline([
        ('poly', PolynomialFeatures(degree=degree)),
        ('std_scaler', StandardScaler()),
        ('log_reg', LogisticRegression())
    ])


# 读取数据
data = np.loadtxt('ex2data1.txt', delimiter=',')
data_X = data[:, 0:2]
data_y = data[:, 2]

# 数据分割
X_train, X_test, y_train, y_test = train_test_split(data_X, data_y, random_state=666)

# 训练模型
poly_log_reg = PolynomialLogisticRegression(degree=2)
poly_log_reg.fit(X_train, y_train)

# 结果可视化
plot_decision_boundary(poly_log_reg, axis=[0, 100, 0, 100])
plt.scatter(data_X[data_y == 0, 0], data_X[data_y == 0, 1], color='red')
plt.scatter(data_X[data_y == 1, 0], data_X[data_y == 1, 1], color='blue')
plt.xlabel('成绩1')
plt.ylabel('成绩2')
plt.title('两门课程成绩与是否录取的关系')
plt.show()

# 模型测试
print(poly_log_reg.score(X_train, y_train))
print(poly_log_reg.score(X_test, y_test))

输出如下：

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2
0.92
0.92

ex2data1逻辑回归（有多项式）.png

ex2data2.txt处理

作散点图可知，这组数据的决策边界绝对是非线性的，所以直接引入多项式特征对ex2data2.txt中的数据进行逻辑回归。

代码实现如下：

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"""
    对ex2data2.txt中的数据进行逻辑回归（引入多项式特征）
"""
from sklearn.model_selection import train_test_split
from matplotlib.colors import ListedColormap
from sklearn.linear_model import LogisticRegression
import numpy as np
import matplotlib.pyplot as plt
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号

# 数据格式：成绩1,成绩2,是否被录取（1代表被录取，0代表未被录取）


# 函数定义
def plot_decision_boundary(model, axis):
    x0, x1 = np.meshgrid(
        np.linspace(axis[0], axis[1], int((axis[1] - axis[0]) * 100)).reshape(-1, 1),
        np.linspace(axis[2], axis[3], int((axis[3] - axis[2]) * 100)).reshape(-1, 1),
    )
    X_new = np.c_[x0.ravel(), x1.ravel()]

    y_predict = model.predict(X_new)
    zz = y_predict.reshape(x0.shape)

    custom_cmap = ListedColormap(['#EF9A9A', '#FFF59D', '#90CAF9'])

    plt.contourf(x0, x1, zz, cmap=custom_cmap)


def PolynomialLogisticRegression(degree):
    return Pipeline([
        ('poly', PolynomialFeatures(degree=degree)),
        ('std_scaler', StandardScaler()),
        ('log_reg', LogisticRegression())
    ])


# 读取数据
data = np.loadtxt('ex2data2.txt', delimiter=',')
data_X = data[:, 0:2]
data_y = data[:, 2]

# 数据分割
X_train, X_test, y_train, y_test = train_test_split(data_X, data_y, random_state=666)

# 训练模型
poly_log_reg = PolynomialLogisticRegression(degree=2)
poly_log_reg.fit(X_train, y_train)

# 结果可视化
plot_decision_boundary(poly_log_reg, axis=[-1, 1, -1, 1])
plt.scatter(data_X[data_y == 0, 0], data_X[data_y == 0, 1], color='red')
plt.scatter(data_X[data_y == 1, 0], data_X[data_y == 1, 1], color='blue')
plt.xlabel('成绩1')
plt.ylabel('成绩2')
plt.title('两门课程成绩与是否录取的关系')
plt.show()

# 模型测试
print(poly_log_reg.score(X_train, y_train))
print(poly_log_reg.score(X_test, y_test))

输出结果如下：

由图可知，分类结果较好。

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2
0.7954545454545454
0.9

ex2data2逻辑回归（有多项式）.png

两份数据

ex2data1.txt

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34.62365962451697,78.0246928153624,0
30.28671076822607,43.89499752400101,0
35.84740876993872,72.90219802708364,0
60.18259938620976,86.30855209546826,1
79.0327360507101,75.3443764369103,1
45.08327747668339,56.3163717815305,0
61.10666453684766,96.51142588489624,1
75.02474556738889,46.55401354116538,1
76.09878670226257,87.42056971926803,1
84.43281996120035,43.53339331072109,1
95.86155507093572,38.22527805795094,0
75.01365838958247,30.60326323428011,0
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39.53833914367223,76.03681085115882,0
53.9710521485623,89.20735013750205,1
69.07014406283025,52.74046973016765,1
67.94685547711617,46.67857410673128,0
70.66150955499435,92.92713789364831,1
76.97878372747498,47.57596364975532,1
67.37202754570876,42.83843832029179,0
89.67677575072079,65.79936592745237,1
50.534788289883,48.85581152764205,0
34.21206097786789,44.20952859866288,0
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61.379289447425,72.80788731317097,1
85.40451939411645,57.05198397627122,1
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30.05882244669796,49.59297386723685,0
44.66826172480893,66.45008614558913,0
66.56089447242954,41.09209807936973,0
40.45755098375164,97.53518548909936,1
49.07256321908844,51.88321182073966,0
80.27957401466998,92.11606081344084,1
66.74671856944039,60.99139402740988,1
32.72283304060323,43.30717306430063,0
64.0393204150601,78.03168802018232,1
72.34649422579923,96.22759296761404,1
60.45788573918959,73.09499809758037,1
58.84095621726802,75.85844831279042,1
99.82785779692128,72.36925193383885,1
47.26426910848174,88.47586499559782,1
50.45815980285988,75.80985952982456,1
60.45555629271532,42.50840943572217,0
82.22666157785568,42.71987853716458,0
88.9138964166533,69.80378889835472,1
94.83450672430196,45.69430680250754,1
67.31925746917527,66.58935317747915,1
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80.36675600171273,90.96014789746954,1
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55.34001756003703,64.9319380069486,1
74.77589300092767,89.52981289513276,1

ex2data2.txt

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作者：@臭咸鱼

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