sklearn逻辑回归实战

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.txtex2data2.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
82.30705337399482,76.48196330235604,1
69.36458875970939,97.71869196188608,1
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
77.9240914545704,68.9723599933059,1
62.27101367004632,69.95445795447587,1
80.1901807509566,44.82162893218353,1
93.114388797442,38.80067033713209,0
61.83020602312595,50.25610789244621,0
38.78580379679423,64.99568095539578,0
61.379289447425,72.80788731317097,1
85.40451939411645,57.05198397627122,1
52.10797973193984,63.12762376881715,0
52.04540476831827,69.43286012045222,1
40.23689373545111,71.16774802184875,0
54.63510555424817,52.21388588061123,0
33.91550010906887,98.86943574220611,0
64.17698887494485,80.90806058670817,1
74.78925295941542,41.57341522824434,0
34.1836400264419,75.2377203360134,0
83.90239366249155,56.30804621605327,1
51.54772026906181,46.85629026349976,0
94.44336776917852,65.56892160559052,1
82.36875375713919,40.61825515970618,0
51.04775177128865,45.82270145776001,0
62.22267576120188,52.06099194836679,0
77.19303492601364,70.45820000180959,1
97.77159928000232,86.7278223300282,1
62.07306379667647,96.76882412413983,1
91.56497449807442,88.69629254546599,1
79.94481794066932,74.16311935043758,1
99.2725269292572,60.99903099844988,1
90.54671411399852,43.39060180650027,1
34.52451385320009,60.39634245837173,0
50.2864961189907,49.80453881323059,0
49.58667721632031,59.80895099453265,0
97.64563396007767,68.86157272420604,1
32.57720016809309,95.59854761387875,0
74.24869136721598,69.82457122657193,1
71.79646205863379,78.45356224515052,1
75.3956114656803,85.75993667331619,1
35.28611281526193,47.02051394723416,0
56.25381749711624,39.26147251058019,0
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
57.23870631569862,59.51428198012956,1
80.36675600171273,90.96014789746954,1
68.46852178591112,85.59430710452014,1
42.0754545384731,78.84478600148043,0
75.47770200533905,90.42453899753964,1
78.63542434898018,96.64742716885644,1
52.34800398794107,60.76950525602592,0
94.09433112516793,77.15910509073893,1
90.44855097096364,87.50879176484702,1
55.48216114069585,35.57070347228866,0
74.49269241843041,84.84513684930135,1
89.84580670720979,45.35828361091658,1
83.48916274498238,48.38028579728175,1
42.2617008099817,87.10385094025457,1
99.31500880510394,68.77540947206617,1
55.34001756003703,64.9319380069486,1
74.77589300092767,89.52981289513276,1

ex2data2.txt

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-0.69758,0.68494,0
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-0.72062,0.53874,0
-0.59389,0.49488,0
-0.48445,0.99927,0
-0.0063364,0.99927,0
0.63265,-0.030612,0

作者:@臭咸鱼

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