Logistic Regression --- Introduction, API Introduction, Case: Cancer Classification Prediction, Classification Evaluation, and ROC Curve and AUC Metrics

一、介绍

1. 大白话~

1. 虽然带有“回归”两个字,But the output result is discrete.
2. 和线性回归的区别,One more activation function（sigmoid函数）,Increase the nonlinear fitting ability of the model.
   

2.损失和优化

逻辑回归的损失,称之为对数似然损失,公式如下：

The loss value can be calculated by the above formula.

二、API介绍

三、案例：癌症分类预测

The point of the case is to use it“逻辑回归”this trainer

import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import classification_report
from sklearn.metrics import roc_auc_score

# 步骤：
# 1.获取数据
# 2.基本数据处理
# 2.1 缺失值处理
# 2.2 确定特征值,目标值
# 2.3 分割数据
# 3.特征工程(标准化)
# 4.机器学习(逻辑回归)
# 5.模型评估 二分类、准确率、精确率、召回率

names = ['Sample code number', 'Clump Thickness', 'Uniformity of Cell Size', 'Uniformity of Cell Shape',
                   'Marginal Adhesion', 'Single Epithelial Cell Size', 'Bare Nuclei', 'Bland Chromatin',
                   'Normal Nucleoli', 'Mitoses', 'Class']
data = pd.read_csv("https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data",names=names)

#2.基本数据处理 缺失值处理（‘？’标记）
data = data.replace(to_replace='?',value=np.nan)  #把‘？’替换成np.nan
data = data.dropna() #删除np.nan

# 划分数据集
x = data.iloc[:,1:10] #特征值
y = data['Class'] #目标值
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)

# 3.特征工程 标准化
transfer = StandardScaler() #实例化转换器
x_train = transfer.fit_transform(x_train)
x_test = transfer.transform(x_test)

# 4.机器学习 逻辑回归建模
# 4.1建立模型
estimator = LogisticRegression()

# 4.2训练模型
estimator.fit(x_train, y_train)

# 5.模型评估 
estimator.score(x_test, y_test)

结果：

0.948905109489051

四、分类评估方法

1. API

2. 例子

Then the above cancer prediction case is written

五、ROC曲线与AUC指标

1. ROC曲线：

1. 先看图片
   
2. 横纵坐标分别是TPR和FPR.那什么是TPR和FPR呢？
   
   那什么又是TP、FP、FN、TN呢？
   
   举个例子就好理解了：
   

2. AUC指标

1. 概念：It is to randomly take a pair of positive and negative samples,正样本得分大于负样本的概率.（To put it bluntly, it is the area of ​​the slashed part in the figure below）
   
2. AUC的最小值为0.5,最大值为1,取值越高越好

AUC计算API

1. API
   
2. 例子：
   Still the next example of cancer prediction：