逻辑回归-乳腺癌肿瘤预测

查看数据集基本信息，去掉异常符号。

import numpy as np
import pandas as pd
from sklearn.datasets import load_breast_cancer# 导入乳腺癌肿瘤预测数据集
data = load_breast_cancer()
X = pd.DataFrame(data.data, columns=data.feature_names)
y = pd.Series(data.target, name='target')# 查看数据集基本信息
print("数据集基本信息：")
print(X.info())# 去掉异常符号
X.replace(to_replace='?', value=np.nan, inplace=True)
X.dropna(axis=0, inplace=True)# 打印处理后的数据集基本信息
print("\n处理后的数据集基本信息：")
print(X.info())

输出结果：

借助LogisticRegression函数和LogisticRegressionCV函数实现回归>逻辑回归。

from sklearn.model_selection import train_test_splitfrom sklearn.linear_model import LogisticRegression, LogisticRegressionCVfrom sklearn.metrics import accuracy_score, precision_score, recall_score, precision_recall_curve,f1_score,classification_reportimport warningsfrom sklearn.exceptions import ConvergenceWarning# 忽略收敛警告warnings.filterwarnings("ignore", category=ConvergenceWarning)# 导入乳腺癌肿瘤预测数据集data = load_breast_cancer()X = pd.DataFrame(data.data, columns=data.feature_names)y = pd.Series(data.target, name='target')# 将数据集拆分为训练集和测试集X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)# 初始化LogisticRegression模型并训练lr_model = LogisticRegression()lr_model.fit(X_train, y_train)# 使用测试集进行预测y_pred_lr = lr_model.predict(X_test)# 输出测试数据个数和预测正确个数test_data_count = len(y_test)correct_predictions_lr = accuracy_score(y_test, y_pred_lr, normalize=False)f1_lr = f1_score(y_test, lr_model.predict(X_test))positive_count = pd.Series(y_pred_lr).value_counts()[1]negative_count = pd.Series(y_pred_lr).value_counts()[0]y_true = y_test  # 在实际情况中，这应该是真实的标签# 生成分类报告report = classification_report(y_true, y_pred_lr, target_names=['class 0', 'class 1'], output_dict=True)# 提取加权平均和算数平均weighted_precision_avg = report['weighted avg']['precision']weighted_recall_avg = report['weighted avg']['recall']weighted_f1_avg = report['weighted avg']['f1-score']macro_precision_avg = report['macro avg']['precision']macro_recall_avg = report['macro avg']['recall']macro_f1_avg = report['macro avg']['f1-score']print("Logistic Regression模型:")print(f"测试数据个数: {test_data_count}")print(f"预测正确个数: {correct_predictions_lr}")print(f"权重: {lr_model.coef_}")print(f"预测结果: {y_pred_lr}")print(f"准确率: {accuracy_score(y_test, y_pred_lr)}")print(f"查准率与查重率：      查准率               查全率               F1_score               support")print(f"   良性          {precision_score(y_test, y_pred_lr,pos_label=1)}   ,  {recall_score(y_test, y_pred_lr,pos_label=1)}   ,  {f1_score(y_test, lr_model.predict(X_test),pos_label=1)}  ,   {positive_count}")print(f"   恶性          {precision_score(y_test, y_pred_lr,pos_label=0)}  ,   {recall_score(y_test, y_pred_lr,pos_label=0)}  ,   {f1_score(y_test, lr_model.predict(X_test),pos_label=0)}   ,  {negative_count}")print(f"   accuracy                                                      {recall_score(y_test, y_pred_lr)}   ,  {len(X_test)}")print(f"   macro avg     {macro_precision_avg}   ,  {macro_recall_avg}   ,  {macro_f1_avg}   ,  {len(X_test)}")print(f"weighted avg     {weighted_precision_avg}  ,   {weighted_recall_avg}   ,  {weighted_f1_avg}  ,  {len(X_test)}")# 初始化LogisticRegressionCV模型并训练lrcv_model = LogisticRegressionCV()lrcv_model.fit(X_train, y_train)# 使用测试集进行预测y_pred_lrcv = lrcv_model.predict(X_test)# 输出测试数据个数和预测正确个数correct_predictions_lrcv = accuracy_score(y_test, y_pred_lrcv, normalize=False)correct_predictions_lrcv = accuracy_score(y_test, y_pred_lr, normalize=False)f1_lrcv = f1_score(y_test, lr_model.predict(X_test))positive_count = pd.Series(y_pred_lrcv).value_counts()[1]negative_count = pd.Series(y_pred_lrcv).value_counts()[0]y_true = y_test  # 在实际情况中，这应该是真实的标签# 生成分类报告report = classification_report(y_true, y_pred_lrcv, target_names=['class 0', 'class 1'], output_dict=True)# 提取加权平均和算数平均weighted_precision_avg = report['weighted avg']['precision']weighted_recall_avg = report['weighted avg']['recall']weighted_f1_avg = report['weighted avg']['f1-score']macro_precision_avg = report['macro avg']['precision']macro_recall_avg = report['macro avg']['recall']macro_f1_avg = report['macro avg']['f1-score']print('\n')print("Logistic RegressionCV模型:")print(f"测试数据个数: {test_data_count}")print(f"预测正确个数: {correct_predictions_lrcv}")print(f"权重: {lrcv_model.coef_}")print(f"预测结果: {y_pred_lrcv}")print(f"准确率: {accuracy_score(y_test, y_pred_lrcv)}")print(f"查准率与查重率：      查准率               查全率               F1_score               support")print(f"   良性          {precision_score(y_test, y_pred_lrcv,pos_label=1)}   ,  {recall_score(y_test, y_pred_lrcv,pos_label=1)}   ,  {f1_score(y_test, lrcv_model.predict(X_test),pos_label=1)}  ,   {positive_count}")print(f"   恶性          {precision_score(y_test, y_pred_lrcv,pos_label=0)}  ,                {recall_score(y_test, y_pred_lrcv,pos_label=0)}  ,   {f1_score(y_test, lrcv_model.predict(X_test),pos_label=0)}   ,  {negative_count}")print(f"   accuracy                                                      {recall_score(y_test, y_pred_lr)}   ,  {len(X_test)}")print(f"   macro avg     {macro_precision_avg}   ,  {macro_recall_avg}   ,  {macro_f1_avg}   ,  {len(X_test)}")print(f"weighted avg     {weighted_precision_avg}  ,   {weighted_recall_avg}   ,  {weighted_f1_avg}  ,  {len(X_test)}")

打印测试数据个数和预测正确个数，打印权重、准确率、预测结果和查准率与查重率：

输出结果：

4.使用不同参数C（正则化强度倒数）的LogisticRegression函数进行实验，设置C=0.1和0.01进行实验。

打印结果：

C=0.1时

C=0.01时

5.绘制ROC曲线：

from sklearn.model_selection import train_test_splitfrom sklearn.linear_model import LogisticRegressionfrom sklearn.metrics import roc_curve, aucimport matplotlib.pyplot as plt# 导入乳腺癌肿瘤预测数据集data = load_breast_cancer()X = pd.DataFrame(data.data, columns=data.feature_names)y = pd.Series(data.target, name='target')# 将数据集拆分为训练集和测试集X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)# 初始化LogisticRegression模型并训练lr_model = LogisticRegression(C=0.1)lr_model.fit(X_train, y_train)# 使用测试集进行预测y_scores = lr_model.decision_function(X_test)# 计算ROC曲线的参数fpr, tpr, thresholds = roc_curve(y_test, y_scores)# 计算AUC（Area Under the Curve）roc_auc = auc(fpr, tpr)# 绘制ROC曲线plt.figure(figsize=(8, 6))plt.plot(fpr, tpr, color='darkorange', lw=2, label='ROC curve (area = {:.2f})'.format(roc_auc))plt.plot([0, 1], [0, 1], color='navy', lw=2, linestyle='--')plt.xlim([0.0, 1.0])plt.ylim([0.0, 1.05])plt.xlabel('False Positive Rate')plt.ylabel('True Positive Rate')plt.title('Receiver Operating Characteristic (ROC) Curve')plt.legend(loc='lower right')plt.show()

运行结果：

6.进行十折交叉验证。

from sklearn.model_selection import train_test_split,cross_val_scorefrom sklearn.linear_model import LogisticRegressionfrom sklearn.metrics import roc_curve, aucimport warningsfrom sklearn.exceptions import ConvergenceWarning# 忽略收敛警告warnings.filterwarnings("ignore", category=ConvergenceWarning)# 导入乳腺癌肿瘤预测数据集data = load_breast_cancer()X = pd.DataFrame(data.data, columns=data.feature_names)y = pd.Series(data.target, name='target')# 将数据集拆分为训练集和测试集X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)# 初始化LogisticRegression模型并训练lr_model = LogisticRegression(C=0.1)lr_model.fit(X_train, y_train)# 进行十折交叉验证cv_scores = cross_val_score(lr_model, X, y, cv=10, scoring='accuracy')# 输出每折交叉验证的准确率print("每折交叉验证的准确率:")for i, score in enumerate(cv_scores, start=1):print(f"折数 {i}: {score}")# 输出平均准确率print(f"\n平均准确率: {np.mean(cv_scores)}")

运行结果：

从上述实验中我们可以看出，在数据集比较小的时候，LogisticRegression模型的分类效果是比LogisticRegressionCV略好的；正则化参数C=0.1时的模型分类结果要好于C=0.01时的结果。

LogisticRegression 是用于二分类问题的线性模型。它通过使用逻辑函数（sigmoid函数）将线性组合的输入映射到0和1之间的概率。训练时，使用最大似然估计来拟合模型的参数，其中损失函数是对数损失。

LogisticRegressionCV 是在交叉验证的框架下执行对回归>逻辑回归的超参数（正则化强度 C）进行自动调优的类。它通过指定一组 Cs 值（正则化强度的倒数）以及交叉验证的折数来寻找最佳的超参数。

两个模型最大的区别就是LogisticRegression是需要手动调参的，而LogisticRegressionCV是自动寻优的，但这并不代表LogisticRegressionCV模型的训练结果就一定比LogisticRegression好，比如本次实验中，由于数据集较小，特征较少，交叉验证结果并不明显，还可能导致过拟合现象。

具体来说，我们可以看到LogisticRegression的分类准确率为0.9649，查准率和查全率分别为0.9672和0.9580；而LogisticRegressionCV的分类准确率为0.9561，查准率和查全率分别为0.9604和0.9464。而且它们分类正确的数据都是110个，所以实际上两个模型的差别并不是很大。

当正则化参数C变化的时候，C=0.1时模型分类正确率为0.96，而C=0.01时模型分类正确率为0.94，显然C=0.1更适合作为当前数据集下的回归>逻辑回归正则化参数，而C=0.01则有点过小了，使得模型有些过拟合。