table of Contents
Questions asked
Two classes based on student achievement data and whether enrollment, students can successfully predict enrollment: use ex2data1.txtand ex2data2.txtdata, logistic regression and forecasting.
Data on the final edge.
ex2data1.txt processing
Scatter as seen, generally follow linear decision, but there are curved (non-linear), linear effect is not good, so two options are available: a program, no characteristic polynomial; Scheme II, there is a polynomial characteristics.
Scheme a: No characteristic polynomial
Ex2data1.txt data in logistic regression, no characteristic polynomial
Code is implemented as follows:
"""
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))
Output:
0.8533333333333334
0.76
Option II: wherein introducing polynomials
Ex2data1.txt data in logistic regression, polynomial features introduced. After debugging, when 3, takes a long time for the degree; when the degree is 2, the acceptable time consuming, compared to the effect of a program with a lot better
To achieve the following:
"""
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))Output is as follows :
0.92
0.92
ex2data2.txt processing
As a scatter plot shows that the decision boundary of this set of data is absolutely non-linear, polynomial introduced directly into the characteristics of the data ex2data2.txt in logistic regression.
Code is implemented as follows:
"""
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))
Output:
The figure shows, better classification results.
0.7954545454545454
0.9
Two data
ex2data1.txt
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69.07014406283025,52.74046973016765,1
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72.34649422579923,96.22759296761404,1
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99.82785779692128,72.36925193383885,1
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50.45815980285988,75.80985952982456,1
60.45555629271532,42.50840943572217,0
82.22666157785568,42.71987853716458,0
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55.34001756003703,64.9319380069486,1
74.77589300092767,89.52981289513276,1ex2data2.txt
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0.63265,-0.030612,0Author: @ smelly salted fish
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