引言
本节主要介绍了逻辑回归方法以及其的应用，并且介绍了分析一个项目的过程与思路， 并以可视化的方式展现，重点在于理解逻辑回归以及其推广到多分类的过程，并学习可视化方式
逻辑回归表达式
逻辑回归，分为logit方程和回归表达式两部分，其为二分类方法，其中logit方程表达式如下，也称为Sigmoid函数：
函数图像如下：
而回归表达式如下：
其中wi的数量取决于特征xi的数量
标准逻辑回归是二分类方程，将其推广到多分类任务时，scikit-learn用的方法是 One vs Rest (OVR) 方法，即每次讲一个类作为正例，其余类作为反例来训练N个分类器，在测试时若某一个分类器预测为正类，则对应的类别标记为最终分类结果。
可视化方式
本例用了许多可视化呈现方式，主要用到的库为 Matplotlib 和 Seaborn库
如下：
- 利用Seaborn画出两两特征影响下各个数据的分布情况
- 画出各个特征的箱型分布图
- 取三个特征画出三维分布图
- 利用Seaborn算出混淆矩阵，并画出
整体代码
'''
机器学习训练营
Task01: 基于逻辑回归的分类预测
Date: 2022-09-18
'''
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.linear_model import LogisticRegression
def demo1():
## 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_cls = LogisticRegression()
lr_cls = lr_cls.fit(x_fearures,y_label) #其拟合方程为 y=w0+w1*x1+w2*x2
## 查看其对应模型的w
print('the weight of Logistic Regression:', lr_cls.coef_)
## 查看其对应模型的w0
print('the intercept(w0) of Logistic Regression:', lr_cls.intercept_)
# 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')
# 可视化决策边界
nx, ny = 200, 100
xmin, xmax = plt.xlim()
ymin, ymax = plt.ylim()
x_grid, y_grid = np.meshgrid(np.linspace(xmin,xmax,nx),np.linspace(ymin,ymax,ny))
print(np.array(x_grid).shape)
print(np.array(y_grid).shape)
z_probe = lr_cls.predict_proba(np.c_[x_grid.ravel(),y_grid.ravel()])
z_probe = z_probe[:,1].reshape(x_grid.shape)
plt.contour(x_grid,y_grid,z_probe,[0.5],linewidths=2,colors='blue')
# 可视化预测新样本
x_fearures_new1 = np.array([[0, -1]])
plt.scatter(x_fearures_new1[:, 0], x_fearures_new1[:, 1], s=50, cmap='viridis')
x_fearures_new2 = np.array([[1, 2]])
plt.scatter(x_fearures_new2[:, 0], x_fearures_new2[:, 1], s=50, cmap='viridis')
# 在训练集和测试集上分别利用训练好的模型进行预测
y_label_new1 = lr_cls.predict(x_fearures_new1)
y_label_new2 = lr_cls.predict(x_fearures_new2)
print('The New point 1 predict class:\n', y_label_new1)
print('The New point 2 predict class:\n', y_label_new2)
y_proba_new1 = lr_cls.predict_proba(x_fearures_new1)
y_proba_new2 = lr_cls.predict_proba(x_fearures_new2)
print('The New point 1 predict Probability of each class:\n', y_proba_new1)
print('The New point 2 predict Probability of each class:\n', y_proba_new2)
plt.show()
def demo2():
import pandas as pd
from sklearn.datasets import load_iris
data = load_iris()
iris_label = data.target
iris_features = pd.DataFrame(data=data.data, columns=data.feature_names)
print(iris_features.head())
print(iris_features.info())
# 利用value_counts函数查看每个类别数量
print(pd.Series(iris_label).value_counts())
print(iris_features.describe())
# 合并标签和特征信息
iris_all = iris_features.copy()
iris_all['target'] = iris_label
# 特征与标签组合的散点可视化
sns.pairplot(data = iris_all, diag_kind = 'hist', hue = 'target') # search
plt.show()
for col in iris_features.columns:
sns.boxplot(x='target', y=col, saturation=0.5, palette='pastel', data=iris_all) # search
plt.title(col)
plt.show()
# 选取其前三个特征绘制三维散点图
from mpl_toolkits.mplot3d import Axes3D # search
fig = plt.figure(figsize=(10,8))
ax = fig.add_subplot(111, projection='3d')
iris_all_class0 = iris_all[iris_all['target'] == 0].values
iris_all_class1 = iris_all[iris_all['target'] == 1].values
iris_all_class2 = iris_all[iris_all['target'] == 2].values
print(iris_all_class0)
# 提取前三个特征
ax.scatter(iris_all_class0[:,0], iris_all_class0[:,1], iris_all_class0[:,2], label='setosa')
ax.scatter(iris_all_class1[:, 0], iris_all_class1[:, 1], iris_all_class1[:, 2], label='versicolor')
ax.scatter(iris_all_class2[:, 0], iris_all_class2[:, 1], iris_all_class2[:, 2], label='virginica')
plt.legend()
plt.show()
# 开始搭建模型、训练
from sklearn.model_selection import train_test_split
iris_feature_part = iris_features.iloc[:100]
iris_label_part = iris_label[:100]
x_train,x_test, y_train,y_test = train_test_split(iris_feature_part, iris_label_part, test_size=0.2, random_state=2022)
# 其拟合方程为 y= w0 + w1*x1 + w2*x2 + w3*x3 + w4*x4
clf = LogisticRegression(random_state=0, solver='lbfgs') # search
# train
clf.fit(x_train,y_train)
# 查看其对应的w
print('the weight of Logistic Regression:', clf.coef_)
# 查看其对应的w0
print('the intercept(w0) of Logistic Regression:', clf.intercept_)
# predict
train_predict = clf.predict(x_train)
test_predict = clf.predict(x_test)
# metrics
from sklearn import metrics
# 利用accuracy（准确度）【预测正确的样本数目占总预测样本数目的比例】评估模型效果
print('The accuracy of the Logistic Regression is:', metrics.accuracy_score(y_train, train_predict))
print('The accuracy of the Logistic Regression is:', metrics.accuracy_score(y_test, test_predict))
# 查看混淆矩阵 (预测值和真实值的各类情况统计矩阵)
confusion_matrix_result = metrics.confusion_matrix(test_predict, y_test) # search
print('The confusion matrix result:\n', confusion_matrix_result)
# 利用热力图对于结果进行可视化
plt.figure(figsize=(8,6))
sns.heatmap(confusion_matrix_result,annot=True, cmap='Blues') # search
plt.xlabel('Predicted labels')
plt.ylabel('True labels')
plt.show()
# 三分类训练和预测
x_train, x_test, y_train, y_test = train_test_split(iris_features, iris_label, test_size=0.2, random_state=2022)
cls = LogisticRegression(random_state=0, solver='lbfgs')
# train
cls.fit(x_train, y_train)
# 查看其对应的w
print('the weight of Logistic Regression:\n', cls.coef_)
# 查看其对应的w0
print('the intercept(w0) of Logistic Regression:\n', cls.intercept_)
# 由于这个是3分类，所有我们这里得到了三个逻辑回归模型的参数，其三个逻辑回归组合起来即可实现三分类。 # 为什么是三组 方程是怎样的？
train_predict = cls.predict(x_train)
test_predict = cls.predict(x_test)
print('The accuracy of the Three Class Logistic Regression is:', metrics.accuracy_score(y_train, train_predict))
print('The accuracy of the Three Class Logistic Regression is:', metrics.accuracy_score(y_test, test_predict))
# 查看混淆矩阵 (预测值和真实值的各类情况统计矩阵)
confusion_matrix_result = metrics.confusion_matrix(y_test,test_predict)
print('The confusion matrix result:\n', confusion_matrix_result)
# heatmap
fig = plt.figure(figsize=(9,6))
sns.heatmap(confusion_matrix_result, annot = True, cmap='Blues')
plt.xlabel('Predicted labels')
plt.ylabel('True labels')
plt.show()
if __name__ == "__main__":
# demo1()
demo2()
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