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函数实现逻辑回归。
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression, LogisticRegressionCV
from sklearn.metrics import accuracy_score, precision_score, recall_score, precision_recall_curve,f1_score,classification_report
import warnings
from 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_split
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import roc_curve, auc
import 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_score
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import roc_curve, auc
import warnings
from 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。