机器学习算法(一): 基于逻辑回归的分类预测

Logistic回归虽然名字里带“回归”,但是它实际上是一种分类方法,主要用于二分类问题,利用了Logistic函数(或称为Sigmoid函数),函数形式为:
l o g i ( z ) = 1 1 + e − z log_i(z) = \frac{1}{1+e^{-z}} logi(z)=1+ez1

Step1:库函数导入

##  基础函数库
import numpy as np 

## 导入画图库
import matplotlib.pyplot as plt
import seaborn as sns

## 导入逻辑回归模型函数
from sklearn.linear_model import LogisticRegression

Step2:训练模型

##Demo演示LogisticRegression分类

## 构造数据集
x_fearures = np.array([[-1, -2], [-2, -1], [-3, -2], [1, 3], [2, 1], [3, 2]])
y_label = np.array([0, 0, 0, 1, 1, 1])

## 调用逻辑回归模型
lr_clf = LogisticRegression()

## 用逻辑回归模型拟合构造的数据集
lr_clf = lr_clf.fit(x_fearures, y_label) #其拟合方程为 y=w0+w1*x1+w2*x2

Step3:模型参数查看

##查看其对应模型的w
print('the weight of Logistic Regression:',lr_clf.coef_)
##查看其对应模型的w0
print('the intercept(w0) of Logistic Regression:',lr_clf.intercept_)
##the weight of Logistic Regression:[[0.73462087 0.6947908]]
##the intercept(w0) of Logistic Regression:[-0.03643213]

Step4:数据和模型可视化

## 可视化构造的数据样本点
plt.figure()
plt.scatter(x_fearures[:,0],x_fearures[:,1], c=y_label, s=50, cmap='viridis')
plt.title('Dataset')
plt.show()

Step5:模型预测

##在训练集和测试集上分布利用训练好的模型进行预测
y_label_new1_predict=lr_clf.predict(x_fearures_new1)
y_label_new2_predict=lr_clf.predict(x_fearures_new2)
print('The New point 1 predict class:\n',y_label_new1_predict)
print('The New point 2 predict class:\n',y_label_new2_predict)
##由于逻辑回归模型是概率预测模型(前文介绍的p = p(y=1|x,\theta)),所有我们可以利用predict_proba函数预测其概率
y_label_new1_predict_proba=lr_clf.predict_proba(x_fearures_new1)
y_label_new2_predict_proba=lr_clf.predict_proba(x_fearures_new2)
print('The New point 1 predict Probability of each class:\n',y_label_new1_predict_proba)
print('The New point 2 predict Probability of each class:\n',y_label_new2_predict_proba)
##TheNewpoint1predictclass:
##[0]
##TheNewpoint2predictclass:
##[1]
##TheNewpoint1predictProbabilityofeachclass:
##[[0.695677240.30432276]]
##TheNewpoint2predictProbabilityofeachclass:
##[[0.119839360.88016064]]

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