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【数据挖掘】贝叶斯分类学习—NaiveBayes

news 来源：原创 2025/6/29 6:38:08

NaiveBayes

朴素贝叶斯的核心是贝叶斯定理，它描述了如何根据新证据更新事件的概率。

要求：

1、实现朴素贝叶斯分类算法，验证算法的正确性，并将算法应用于给定的数据集Data_User_Modeling数据集，选择一部分数据集作为已知结果，然后用剩下的数据集作为测试集，验证算法的分类情况

2、重新选取训练样本和测试集，对比并分析分类结果

3、选取一部分数据集作为训练样本，实现分类；不断从测试集中选取数据加入到训练集中，对比并分析分类结果

代码实现：

import pandas as pd
import numpy as np
from math import pi, sqrt, exp# ========================== 数据预处理 ==========================
# 配置文件路径（请根据实际路径修改）
DATA_PATH = r"D:\课程\数据挖掘\实验四\实验4-Data_User_Modeling_Dataset_Hamdi Tolga KAHRAMAN.xls"# 读取Excel数据
excel_file = pd.ExcelFile(DATA_PATH)
df = excel_file.parse('Training_Data')  # 假设工作表名为'Training_Data'# 数据清洗：统一目标变量格式（转为小写并去除空格）
df['UNS'] = df['UNS'].str.strip().str.lower()# 划分训练集和测试集（70%训练，30%测试）
train_df = df.sample(frac=0.7, random_state=42)
test_df = df.drop(train_df.index)# 分离特征和标签
X_train = train_df.drop('UNS', axis=1)
y_train = train_df['UNS']
X_test = test_df.drop('UNS', axis=1)
y_test = test_df['UNS']# ========================== 朴素贝叶斯算法实现 ==========================
class NaiveBayesClassifier:def __init__(self):self.classes = None       # 存储类别标签self.mean = {}            # 各特征在类别下的均值self.var = {}             # 各特征在类别下的方差self.prior = {}           # 类别先验概率def fit(self, X, y):"""训练模型，计算类别统计量"""self.classes = np.unique(y)  # 获取所有类别n_samples, n_features = X.shape  # 样本数和特征数for cls in self.classes:cls_data = X[y == cls]  # 提取当前类别数据self.mean[cls] = cls_data.mean(axis=0)  # 计算各特征均值self.var[cls] = cls_data.var(axis=0, ddof=1)  # 计算无偏方差（ddof=1）self.prior[cls] = len(cls_data) / n_samples  # 计算先验概率def _gaussian_probability(self, x, mean, var):"""计算高斯分布的概率密度函数（连续特征）"""exponent = exp(-((x - mean) ** 2) / (2 * var))denominator = sqrt(2 * pi * var)return exponent / denominatordef predict(self, X):"""预测样本类别"""predictions = []for _, sample in X.iterrows():posteriors = {}for cls in self.classes:# 计算先验概率（取对数避免下溢）prior = np.log(self.prior[cls])# 计算似然概率（特征独立假设，乘积转对数求和）likelihood = 1.0for feature in X.columns:prob = self._gaussian_probability(sample[feature],self.mean[cls][feature],self.var[cls][feature])likelihood *= prob if prob != 0 else 1e-10  # 处理零概率# 后验概率 = 先验概率 * 似然概率（取对数域计算）posterior = prior + np.log(likelihood)posteriors[cls] = posterior# 选择后验概率最大的类别predictions.append(max(posteriors, key=posteriors.get))return np.array(predictions)# ========================== 模型训练与评估 ==========================
# 创建分类器实例并训练
nb_classifier = NaiveBayesClassifier()
nb_classifier.fit(X_train, y_train)# 预测测试集
y_pred = nb_classifier.predict(X_test)# 计算准确率
accuracy = np.sum(y_pred == y_test) / len(y_test)
print(f"朴素贝叶斯分类准确率: {accuracy * 100:.2f}%")# ========================== 可选：增量学习实验（按实验要求扩展） ==========================
def incremental_learning_evaluation(initial_train, test_data, steps=5):"""逐步将测试数据加入训练集，观察准确率变化"""train_data = initial_train.copy()X_incr = test_data.drop('UNS', axis=1)y_incr = test_data['UNS']n_test = len(X_incr)step_size = n_test // steps if n_test >= steps else n_test  # 避免除数为0for i in range(steps):start_idx = i * step_sizeend_idx = (i + 1) * step_sizeadd_X = X_incr.iloc[start_idx:end_idx]add_y = y_incr.iloc[start_idx:end_idx]# 合并训练数据train_data = pd.concat([train_data, pd.concat([add_X, add_y], axis=1)])current_X_train = train_data.drop('UNS', axis=1)current_y_train = train_data['UNS']# 重新训练模型incr_classifier = NaiveBayesClassifier()incr_classifier.fit(current_X_train, current_y_train)# 预测剩余测试数据remaining_X_test = X_incr.iloc[end_idx:]remaining_y_test = y_incr.iloc[end_idx:]if not remaining_X_test.empty:y_pred_incr = incr_classifier.predict(remaining_X_test)current_accuracy = np.sum(y_pred_incr == remaining_y_test) / len(remaining_y_test)print(f"加入{end_idx}条数据后准确率: {current_accuracy * 100:.2f}%")else:print("所有测试数据已加入训练集")# 执行增量学习实验（可选，取消注释后运行）
# incremental_learning_evaluation(train_df, test_df, steps=5)